Coolant, Transmission Fluid and Brake fl change interval?

FWIW Is it too long?
If not DIYing, just follow the manual.
If DIYing and you consider "wrenching" as a hobby, cut the time/ mileage in half.
The flush will aid in removing any "scum" buildup and new coolant has fresh rust/ corrosion inhibitors, which may prevent coolant passage issues.
PS I'd advocate using bottled distilled water for the system flushing.

FWIW Brake Trans & Brake?
Old school servere-duty trans fluid changes; many said at 20K mileage.
I DIY'd mine at 40K and the fluid had a darkness and I noticed an improvement with new fluid.
Brake fluid absorbs moisture over time.
Again, many say it should change every two years.
I recall there was a Toyota Owners manual that referenced every 3 years.
Getting the water out can extend the life of all the metal lines.
Plus with a new fluid flush and its related line debris and air purging, your brake pedal feel should improve.
However, if DIYing, be aware of the precautions; do a search.

Have fun

 

Regarding the longer inverter coolant change interval: Toyota Canada says to change both at 10 years or 160k kms (~100k miles), whichever comes first. I emailed them to verify, in consideration of this sticker, on the inverter coolant reservoir of our Canadian spec 2010:

pic to come

Toyota USA says nothing about either. Toyota Canada at least specs a brake fluid change interval (starting around model year 2014). It's 3 years or 48k kms (~30k miles), whichever comes first.

Neither Toyota USA or Canada say anything about transaxle fluid change. I would recommend an early change, say around 1 year or 10k miles, then one more around 50~100k miles. This is judging from the appearance of the drained oil, with the several drains I did: it got progressively cleaner looking, to where I figured I was wasting my time.

If you're thinking to DIY any of these I can post some Repair Manual excerpts. There's also some relevant links in my signature, 3rd gen specific, but quite similar. (on a phone turn it landscape to see signatures)

 

It's (3) 10mm bolts along the lip spoiler and a bunch of plastic rivets - not that difficult. Don't you remove the access panel to do oil changes? It's no more difficult than that; just more plastic rivets.
Normal, old style non-severe duty ATF changes were usually around 60K miles. Truck, heavy duty, and towing was 30K miles or less. These eCVTs really don't fail that much, but if your planning to drive that car until the wheel fall off - I'd change it sooner, rather than later. After the first change, you should be able to go 60K-100K miles before the next change - the first one is usually the dirtiest. While there isn't a change interval, the manual does say check it. How and what to look for or test is a mystery.
I go with a 5 year flush interval on the brake fluid, even if it test good. Moisture and contaminants will jam up that brake by wire system, so pushing all that junk out of it should keep that from happening. Braking systems are also pretty robust, it'll just take you longer distances to come to a complete stop. That's if the ECU will allow the car out of limp mode, depending on the severity of the ABS error.

Hope this helps.......

 

Whaaaat?

Whenever you remove the plastic fasteners, take care with the process, and before reinstall: sluice them thoroughly in soapy water and rinse well. Replace promptly if they break (genuine Toyota best option). For any bolts, oil coat them.

 

1) ATF: "the first one is usually the dirtiest" - why?
Does this car has a dipstick for the Tranny?
Assuming its never been done, what should be my plan going forward?
It's really up to you, since I error on the side of caution and know that fluids don't last forever. There's no dipstick, two 10mm hex plugs. One plug at the base, facing the drivers side - drain. Another facing passenger side, up near the half-shaft output. Warning, They are really tight out of the factory. Recommend a 10mm hex socket and 36 inch breaker bar - DO NOT round them off.
I did an early ATF change on both 2012 Prius C and current 2021 Prime at around 20K; both looked like they had many more miles on them. I was only able to do a second ATF change on the Prius C @ 90K before an uninsured motorist totaled it out. That drain and fill was much cleaner than the initial one. I can only surmise that it was mostly break-in material and assembly dirt on the original drain. Didn't send it out for testing - just my observations. I did post pictures of my 2021 Prime ATF change a while back.
There may be (4) 10mm screws attached to that lip spoiler. It's fairly obvious once the car is up on ramps. Hint, the screws come out last - reverse order when putting up that plastic belly pan. Putting the screws in first will align the plastic rivet holes, so you can work your way towards the rear of the car - inserting and locking those plastic rivets in place.

2) BF - 5 year flush.
The PepBoys do them for about $80? Or find a private mechanic?
I do not touch the brake stuff.
I would question them to make sure it's an actual flush. I've know shops to suck out the brake reservoir, refill and call it a flush! That is NOT a flush, though some here would argue that it is. I switch between a blue DOT3 and normal DOT3 brake fluid. That way I know my lines are clear of the old stuff.

Hope this helps....

 

The ones mentioned so far, attached. If anything else comes to mind, just let me know.