Cable is pretty much out of the question. All the conduit through the slab to outside the house is occupied (shop subpanel, well pump, etc). Radiant heat in the slab rules out drilling, and that wouldn't help anyway because the utility room is 20' from the outside wall, and the stemwall is 2' thick concrete.
No way to put the powerline adapters on the same breaker - the shop is on a subpanel served by a dedicated breaker.
Looks like an RF bridge is the way to go. Even with the RF link on the wall of the shop, there's still the problem that the building is all metal - a Faraday cage.
Uh, it may not be practical in your location, to get folks/equipment with right experience and tools, but none of what you listed would prohibit drilling and running a new conduit under the slab and through 2ft of concrete if required ... which would be what I'd be looking into... but could be price prohibitive, especially in a remote area ?? ...
Personally, with 90meter Ethernet standard (+5m for either end for patch cord), I'd consider less direct path... ie running through attic to preferred exterior house location (ideally with easy access to bring cable down wall, either interior wall, or closet, or ??) as noted, you have 300+ft of cable length to work with, sometimes a less direct route isn't as hard? then if you can rent tools that let you burrow a new conduit run under a slab for that relatively short distances required? and how deep is that stem wall? go under it?
that said, a point to point wireless ethernet bridge would work fine, and simply put a shade cover over it. And considering alternative, though annoying, simply be prepare to replace every 3-5 years... such gear isn't expensive. but beware cheaply made consumer gear, ex anything by TP-link (not too mention security issues ... granted my exposure was many years ago, but eye-opening to participating in 3-letter agency cyber-security briefings... tech conferences, etc open to public. Personally, if I was given free TP-link gear (and many other similar mfgs) the only thing I'd consider is giving away to an enemy, or outright destroying)