These “what cable should I use threads” always bring out all kinds of opinions, none totally wrong with some more opinion than fact.
As usual,
@wyliesdiesels is recommending a very nice product. I’ve also used it and it will work great in this case. It isn’t inexpensive but it will be a lot simpler than fiber. Like he said, lightning is an issue when you run a cable from one building to another. Fiber eliminates this concern as does a point to point link. If you have conduit to use do not even think about a point of to point link no matter what anyone says.
I’ve use all kinds of gel filled outdoor cable and some have been better to use than others. I’ve also installed PVC jacketed Cat5e in places where an outdoor cable would have been better and most are still working after a decade or more. Not all, but most. Having conduit gives you the flexibility to pull something cheap (like some Cat5e) for now and upgrade later if you feel the need to do so. Most people will never be able to utilize the capabilities of anything better than Cat5e unless you’re doing a lot of data transfers or streaming multiple 4k streams at the end of that cable. Cat5e is capable of Gigabit speeds but Cat6 is better. Cat6a is not needed for what you’re doing.
Find yourself a chunk of direct burial Cat6, run 2-3 of them in one of the conduits and move on to other projects.
When going between buildings with copper wire I like to put a cheap 5 port switch at each end to act as a sacrificial device should something happen. There are actual surge suppression devices out there that are more proper to use but a cheap 5 port switch works okay and can be used as a switch as well.
Have fun with the project and keep us updated !