Fair cost to replace a tire and sensor for prime LE?

There is no such thing as a universal "fair price" for anything.
It depends mostly on where you live.......and you appear to be in a "high cost" area.

You have some warranty information along with your Owners Manual.
In there is a number to call with warranty questions.
Use it.

 

Yeah, going to a dealer for tire and TPMS issues was your biggest mistake. They do price gouge. Tires are not covered by Toyota warranty. The tires are covered by a separate warranty from the tire manufacture, in this case Toyo, but OEM tires do not usually have the road hazard coverage. TPMS sensor should be covered by Toyota basic warrenty if found defective, but if the damage is due to flat tire, then warranty would not cover it. Toyota care is only for road side assistance service (i.e. towing to a nearest dealer). It does not cover any cost for diagnosis or repair.

The Toyo Nano tire is ~$90 online. The TPMS sensor should not be damaged by simple flat tire. It is at the base of the valve stem inside of the rim. Unless you really wracked the rim, I can't imagine it can be damaged. That being said, if it is malfunctioning and need to be replaced then the OEM sensor is $91.34 MSRP, but can be found anywhere from $20 to $65 online. Mount and balance a tire and reprogram a sensor for one tire should cost $20 top. Total cost (a tire, a TPMS sensor, and labor) should be anywhere from $130 to $200. Anything above $200, you are being ripped off.

 

Buy new cars at a place that sells new cars.
Buy new tires at........

BTW
The TPMS sensor "maybe" being bad is probably balloon juice....but I'm kinda curious.
You said you TOOK your car to the dealership.
How?
If you drove it there, then you're either one of those few remaining people who consider a spare tire to be important - OR - you slimed your car or drove it to the dealer with much less than the recommended amount of air in your tire.

Either way?
YOU know that your tire had a nail in it.....

THIS means that you're an exceptionally talented driver who regularly checks their tire pressures OR you noticed by the way your car handled that one of you tires was low.
Or....
Perhaps.....your Tire Pressure Monitoring System informed you.
If the latter is the case then this points away from a damaged sensor.

So....
I'm not gonna shame you into admitting that you don't drive with a proper spare, but if Toyota's tire-repair kit somehow damages their TPMS this would be................."interesting."
I'd find out about that.
Especially in California.
I do not mean to state-shame you or anything but you guys have potholes out there big enough and they have been around long enough to have names in Google Maps.

ToyotaCare takes care of.......TOYOTA.
They WANT you to maintain a closed-hood maintenance philosophy so that you're "encouraged" to bring the car back to THEM so that they can over-charge you for some things (tries, batteries, filters, etc...) and also shank you for some unneeded maintenance and repair items......

TPMS sensors....for example.