Find a different shop and replace the head gasket on your existing engine. It’s not a big deal to replace a head gasket on a Prius engine, the gas engine is just a regular simple 4 cylinder engine.

You do not want a used Japan import engine. The way the auto market works in Japan is that cars are taxed much more heavily as they age, as a way to strongly incentivize people to replace their cars after only a few model years. One side effect of this is that you end up with a lot of cheap used engines from cars that are more than about 5 years old. A bigger issue here though is that nobody maintains their engines, because they only need to last them a couple years. The Japan used import engines often have never had an oil change! Suffice to say, don’t buy one of if those engines, just get a different shop to change your head gasket. You are right when you say that it’s not a big deal to change a head gasket.

How many miles are on it? Some of these engines are known for consuming oil which might get worse with a fresh head.

I am presently looking at the ltest revision of the relevant TSB (EG-00573T-TME) from Toyota regarding head gaskets for all ZR family engines. The only “special” recommendation is to use the new redesigned parts that became available in 2021 (-FE/-FAE) and 2022 (-FXE).

Unless your engine is using a lot of oil (common with early 2ZX-FXE at high mileages) or has some other issue, replacing the whole engine makes sense only if you get an absolutely smoking deal on the engine swap. Otherwise this sounds like the typical sod off quote.

I work in a repair shop and we will do head gaskets, a lot of others won’t though because liability, in some rare cases the repair fails, we have had a few fail, and it turns out the issue is a hidden crack or something, of course then the customer is angry and it all goes sour because we don’t have xray vision and sending out for crack and pressure testing is expensive.

This is why they don’t want to get involved, selling an engine with a warranty protects them.