Any diagnostic software that will hint if headgasket will be needing replacement soon?

you can check the egr electronically, but not the head gasket, afaik. i think you need a boroscope or leakdown test.
have you cleaned the egr circuit? oil every 5k? are they all hv miles?

also, with a 2014, you should research whether you have the old or new pistons and rings

 

How much of the miles are electric-only?

That said, if it were a reg 3rd gen Prius, odometer reading is pretty much all the software you need; with 165k it’s cleaning time. And if you’re losing coolant and/or getting cold-start shakes: leak down test and boroscope inspection.

tips and links in my signature.

 

Excessive oil consumption is a sign as it clogs and carbons the cylinders faster. A vin with the last six digits higher than 055768 is a positive as your 2014 would have the updated pistons and rings.

 

looks normal to me.

a number of things can contribute to lower mpgs. tires, 12v, filters, plugs, weather, driving distances, topography, clogged hv cooling fan and etc.

unfortunately, if you have tracked ev/hv miles, there is no way to go back and get it. do you plug in regularly?

does she burn any oil between changes? is the coolant level stable?

when the cleaned the egr, did they clean the 4 small ports in the intake manifold? very important, and most dealers don't know it.

 

Old Skool diagnosis:
If you put your foot down and you see:
white smoke it’s water/coolant
black smoke it’s oil

 

You will get occasional startup rattles and shakes long before white smoke starts. Sometimes months before. So startup rattles and engine shaking is the early warning. It will sound really bad like you threw a rod, metal to metal and then go away and run fine. By the time white smoke appears it will be shaking and rattling when taking off from stop lights after one or two minutes.

 

Maybe try the chemical test of coolant system for CO2 leaking from the combustion chamber.
Most speed shops sell these kits.