Powerline Wifi Extender

Run you an ethernet cable from the house (can go max length ~328'). You don't need to dig a deep trench or anything just use the one rated for burial and put it down 2-3". Its cheap if you ever have an issue and having an ethernet cord run with a router out there will be so much nicer in the long run.

Powerline adapters work and are built basically exactly for your use case. Hopefully your shop is wired 240v and has both sides of the split phase available as wall outlets. Otherwise 50/50 chance you can’t plug the inside end near your Ethernet router/hub. That’d be a dealbreaker. Also speeds are rather terrible but probably fine for a shop.
I would rather:
1. Just spend $50 on eBay and get an outdoor mesh node compatible with my WiFi system.(Deco makes them) or just an extra $20 cheap node may work depending on building material.
2. Bury Ethernet and connect to compatible mesh node given there is a manageable burial path.

If you don’t already have a mesh WiFi system, you will want one(even with powerline) so that your internet is seamless between buildings.
If no WiFi mesh system, you could also just get a nearly free WiFi extender/bridge or a powerline to WiFi adapter(as part of the powerline set) but then you are more janky then seamless.

100 feet on a different circuit, you'll probably get less than 1mbit FYI.

Those things are basically useless.

And never just pull one cable. Cable is cheap.

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Dig a trench and run fiber.

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I wasn’t going to recommend that on this forum but now that the cat is out of the bag, yes. Much more future proof too as multi gig fiber in the home is about half the price of copper right now. Cables are about the same but SFP+ modules are like 3x-4x cheaper for fiber.

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Thanks for the feedback. Looks like running a fiber line to the shop is the best way to go in the long run.

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I wouldn’t go that far, but in long run it’s a better solution.
Pros: future proof. Does not rely on robust grounding between house and shop. Significantly cheaper than copper for 5g-40g speeds. Will be good 20-30 years from now.
Cons: $30-300 more expensive than copper for 1g speeds (depending on level of thrift). Fiber cable will not withstand crushing and bending, making a burial installation much more challenging. May want to thrift some conduit or use fine sand for fill. Indoor fiber is same price as copper but direct burial vs indoor cable cost goes down for copper(less fire resistance) and up for fiber(added armor). Also need to buy correct fiber length as you won’t be cutting your own.

Really depends on your skill set, what supplies you have lying around, what your current wireless setup is, and level of effort you’re willing to put in. You may be able achieve your goals with a decently planed WiFi system and avoid all the hassle.