Let’s say I blocked a user indefinitely for three strikes on The Sims Wiki (I’m not an admin over there but I’m giving an example) but can I also apply the block over to Battlefield Wiki? They’re both games made under the same company.
You can; as an admin you can block people for any reason. Including no reason. I would advise you don't, though. If the person is inactive on the other wiki, it seems petty. If they are, but have not had their three strikes, that seems unfair. Three strikes isn't a set universal rule, but if you use it, you've got to use it consistently. If you just want to prevent drama, that's easy enough to stifle once it starts.
I've blocked people that I later had to block on other wikis. I've blocked people that worked fine on other wikis.
If you can justify it to yourself, block them. If you can't... don't. Or do. In the end, it's your call.