2023 Prius Prime SE - TPMS Schrader 33500 EZ

I think it's in the manual. There's a whole section on it with a lot of blah blah in it.
Here's only one page, for rotation.
I think it's needlessly complex.

 

The car can remember two sets of tyres. It is capable of detecting new sensors without special tools, but only they're if they're of the newer type.

From the "so long as they are programmed at installation" note, yours are presumably of the older type, which would mean it can't detect them from scratch.

Given that the car is apparently not listening to these sensors, your best hope is that installers DID program the codes in, as they were supposed to, but they helpfully programmed them into the blank spaces for the second set, rather than overwriting your initial set.

But they did that without actually selecting the second set, which you should be able to do now.

Procedure for that is in a page close to the one posted above - "Selecting wheel set". Menu entries TPWS Setting -> Tyre Set Switching -> Register Valve / ID -> Tyre Set X.

If you flip that, maybe it will start working. (After maybe 5 minutes of driving).

If not, try flipping back to the other set, and then try the rotation thing above.

Last resort before going back to the installers would be try a from-scratch registration as per the section "Registering ID codes", but I would not expect that to work with the sensors you have.

(And I would be concerned that using that menu entry would make it forget a sensor set, thus forcing you to go back to the dealer to reprogram the old-style ones. Take care not to use it on the old sensors' set when you get them working. But maybe it's sensible enough to not blank codes unless it sees some new codes to replace them with.).

Car Care Nut video about the two Toyota sensor systems, which may be helpful:

 

Watching video-it is 4 years old.
Brings back memories of the Ford Exploder.
edit: It looks like that Schrader needs a scan tool:
https://www.schradertpms.com/en/our-products/schrader-ez-sensor-familyr

Too bad, because non-OEM direct replacements are available.
This is what I came up on Amazon for a '25 Prius: