EGR intake cleaning and also 100,000 maintenance really required

you are right at the blown head gasket mileage, it is absolutely imperative to clean the entire egr circuit. and i would add an occ as well.
there's not much to 100k regular maintenance, do you have a schedule?

i would also change the tranny fluid

 

The car will tell you how well the EGR is flowing if you ask it. It runs that test routinely while you are driving, so when you ask, it just gives you the most recent test result. We have a thread about that.

You can ask with any basic scan tool (or phone app with a car diagnostic dongle) that is able to do monitor test status ("mode 6") queries. You can get those for cheap and they can be very valuable to have around, even you hire out most of your mechanical work. A recent thread is a good review of several of those. (It has details specific to Prius Gen 2, but should be useful in broad strokes.)

We've been seeing test results around 21 or 22 kPa for freshly-cleaned EGR systems. I cleaned mine at around 15x,000 miles, when my reading was down to 10 point something. Based on your driving and other factors, yours could be clogging at around the same rate, or not as fast, or faster. The test result will tell you. You also might decide the 10 point something threshold I used was too daring for you, or not daring enough. We really don't know enough yet to say how low is too low. (The test limit threshold where a P0401 code is given is down below 2 kPa, but that's widely suspected here of being longer than you want to wait.)

It is worthwhile to remove just the intake manifold and inspect its four small EGR passages directly. The built-in test can't tell you how those are doing, and the manifold by itself is an easy job (say, ½ hour for someone mechanically inclined).

Overhauling all the rest of the EGR is much more grueling and labor-intensive (and expensive, if you are paying hourly for the work). So it can be sensible to make that call based on what the flow test is telling you.

 

how many miles have you put on since they replaced the egr valve?

cleaning the intake manifold is part of the circuit.

ignore the timing gasket

a lot of gen 3 prius blow the head gasket around 100k or more, due to back pressure from a clogged egr circuit.
occ = oil catch can. it captures some of the blow by from the engine, keeping it from clogging the egr circuit.
along with the pistons and rings, and the brake booster, it is the weak link of 2010 to part way thru 2014, when toyota upgraded the pistons and rings.

watch

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I can't say that any of the "it happens due to X" ideas around here has been really shown yet, and this particular X isn't one I've even seen here before now.

 

See first link in my signature, ditto for OCC.

(if on a phone, turn it landscape to see sig)

 

agreed, senior moment. o/p please ignore the advice of an old man, and listen to chapman.