My 2012 Prius V with 172,000 miles started having the oil light comes on even when the oil is full?

That is new information. One thing to know is Service Advisors at dealerships are usually commissioned salesmen often with no mechanic experience. They try to translate a mechanic's notes to something a typical customer might understand and often lose context in the process.

Shaky starts could be a sign of a problem. The engines have two common shaky start issues; one is a head gasket leak and a second is a sticking open egr valve. Both can be intermittent, eg not every time or even every day.

As a result a dealer mechanic might not experience it.

While unusual, clogged fuel injectors can also cause a shaky start but would normally continue and code as misfires.

The shakes could be bad enough to reduce oil pressure if the oil pump or oil passages were already partially clogged.

However the oil light staying on longer than 5 seconds really is not good. It could fail completely at any time.

 

For a heady moment I thought “huh, $7k (USD) for a new engine, not bad”. Then reality set in.

 

Tina,

You need to start seeing other mechanics.
Immediately.
Like......before you drive it again.
As stated before, 99.44% of the time when you see a red oil pressure light then your engine is the process of destroying itself.

Also, as stated before the "shaky startup" is something else entirely.
It's like chest pain in a human.
It could be gas pains.....or......you might be having a heart attack.

and.....$7,000 for a new, 110,000 mile engine?
Did they say that with a straight face - or is 110,000 miles the warranty period for the new engine??

 

Toyota does not sell new engines. You can buy a new short block and separately get a new head as an assembly but that's about it.