2009 Prius, possibly a bad fuel injector?

My last time on this forum, was when I had an...incident during a routine spark plug change. A quick summary of that situation being that I accidentally shattered a spark plug during removal, and some ceramic pieces fell into the engine. After installing the new plugs, the engine shook and rattled horribly (much like in this video). Shortly after, the engine settled down and I instead only heard a light tapping/rattling (kind of like piston slap or noisy lifters). I took the car to a local shop for diagnosis, where they said that there was ceramic in the engine like I had thought (I attempted to remove ceramic pieces before extracting the old plug) and they claimed that the noise was caused by these pieces. The shop said they attempted to remove them, but that they were stuck to the cylinder head. This is the noise I hear:

Edit 2: Oh, I will also note that the car will shake a little shortly after startup when the motor is cold. It will go away after the motor warms up

A few days ago, I had a discussion with some people on a Discord server about the noise I hear. They told me to run a test by unplugging the fuel injectors and see if the noise would go away. So I did just that. I ran the engine with 3 injectors at a time, moving from left to right. When the engine would kick on, it would shake and rattle like I experienced on the first start with the new spark plugs and sounds similar to the YouTube video linked above; however, when I add throttle myself, the engine would seem to smooth out just fine and I would not hear the sound I normally hear. But this did not seem to be specific to a particular injector/cylinder. I will note that when I had the right most injector unplugged, the engine stalled out shortly after starting up. The engine ran the worst when that injector was unplugged.

I may remove the spark plugs to check the gap, inspect them for damage, and see if they are wet/blackened. However, I refuse to attempt removal until I get a magnetic spark plug socket. Last time, removal went poorly with my cheap rubber booted plug sockets. I was also thinking about performing a compression test on each cylinder just to check engine health. Oil consumption seems to be well within Toyota's spec listed in the manual. I did not see any CELs or other abnormal lights during my testing. I do not have a code reader though, so its possible I just didn't see them. Someone on the same Discord (but unrelated to the previous discussion) thinks that my car is not picking up misfires; but I cannot confirm without a code reader. Edit: the car is at about 101k miles. The...incident....occurred at around 97 or 98k, conveniently right after my last oil change.

My question(s) here is this:
Am I onto something here? Is it possible that one or more of my injectors is going bad? Should I run injector/fuel system cleaner? Or maybe a spark plug is damaged? Or is it just the ceramic pieces as I original thought? I will note that my average fuel economy has dropped by 2mpg from where it would normally be this time of year. My thinking here is that if the ceramic pieces are stuck to the cylinder head, would they really create any noise?

I know the head will probably have to come off to get the ceramic pieces out, which if a compression test comes back good then I will probably wait on that.

I appreciate any feedback, I'm still quite new to working on cars; particularly on those with fuel injection and piston engines.

 

Thanks for the tip on inspection mode, I'll look it up.

I originally thought that it might be something mechanical, but with the crazy noise it makes just by unplugging one injector and based on the noise in the linked YouTube video, I'm not entirely sure. I will likely get a borescope if it ends up coming to that.

The people I originally talked with on Discord got back to me and are thinking it might be a fuel pressure related problem. When I was free revving the motor, the ticking/tapping would go away. Which when firing only 3 injectors, low fuel pressure wouldn't be a big problem. Is there an easy way to check the fuel pressure?

 

The plot thickens.....
I ran below a quarter tank of gas, so I threw in a can of Seafoam in case maybe my fuel system was clogged a bit or one of the injectors was dirty. I drove around quite a bit with basically no change in the sound.

I put the car in inspection mode and just started listening and taking video. Some people on Discord were saying it sounds like it might actually be valvetrain related. After some research here on the forums, I'm inclined to believe that; but with how many twists and turns this story has, I am hesitant to commit to any one possibility.

When listening to the engine from underneath the car, it sounds like its pinging, possibly like detonation (never heard detonation before, so I can't say for certain). It is below a half tank with a full can of Seafoam mixed with the fuel though, so it could simply be that; or the ceramic pieces are responsible for that noise. I might put in a higher octane fuel grade at the next fill up as well.

Presently, I've decided to forgo testing fuel pressure. I'm going to get a long extension and start listening around the motor, try and better pinpoint the source of the sound. I also plan on running a compression test, and of course inspecting the spark plugs and coils while I'm at it. The coils are the original, and replacing coils seems to have helped people on here in the past, but I am hesitant to fire the parts cannon at this stage. Once I get the plugs out and get compression numbers, as well as a likely source of the sound, I think I'll better be able to come up with a solid theory.

Right now, I'm thinking that the ceramic shards may have thrown a valve out of clearance. Could also just be pure coincidence that a valve decided to go out of spec at a convenient time. Of course, it also could just be that the lifters decided to become angry and nothing is really wrong. I will probably contact a dealer and/or some local shops to see about maybe getting the valves clearanced, or at least inspected; maybe get the head taken off to get the ceramic out as well, but will depend on quotes.

Here's my recent video footage:

I appreciate the suggestions so far, and inspection mode is a huge help.
Unrelated comment: I hate working on this car, lmao. Piston engines are so much more complicated than rotary engines.

 

I don't see any abnormal lights on the dash. I would check the computer, but lack a code reader. I ran some Seafoam in the gas just to see if it helped, but starting to think fuel is unrelated at this point.

I'm new to really trying to care for fuel injected cars, so I'll keep that tip about regularly running cleaner in mind.

 

Quick update:
I played doctor with some socket extensions and the noise is somewhat noticeable if I put the extension at the bottom end, but it was extremely faint. Placing the extension on the top of the engine, the noise is very noticeable, particularly around cylinder 1 and 2. Putting the extension anywhere else and I could not hear it at all. I'm fairly certain it has to be valvetrain at this point.

I took the spark plugs out, the tips looked decent enough but a little dark. The threads were very oily for some reason. While I had the plugs out, I performed a compression test. For some reason my tester wouldn't hold the compression after the engine stopped, but it did peak at around 150psi on cylinders 1, 3, and 4. Cylinder 2 peaked at around 140psi. I'd have to get a camera to see if the walls are scored, but I doubt it. Considering the valvetrain is making a lot of noise, its most likely a valve related problem. I'm going to call around some local shops next week and get a quote on valve clearancing. We'll see what they say, but I'm sure it will be cheaper than a new motor. I will probably also ask them to check the rest of the engine with a borescope as well since they'll already be working in there. Maybe even ask if I can take a peek for myself, or at least get texted/emailed some photos.

Some codes seem to have come up in the process of the compression test, since the red triangle and the CEL are on. I'm confident that they are probably misfire codes and charging issue since the motor was cranking over with no plugs/coils or injectors. Waiting to hear back from a friend with a code reader so I can confirm them and have them cleared. Just for the hell of it, I'm going to put a majority higher octane fuel in when I go fill up.
EDIT: I stopped for gas, put in 7 gallons of 89 and a gallon of 87. When I started the car back up, the red triangle and CEL were gone. Regardless of what they actually were, seems my suspicions were correct. Will probably update once I decide on what to do about the valve work.