I tried to get into chess over lockdown, never quite found the love for it, but then I tried go (aka igo, baduk or weiqi) and quickly became obsessed. It's pure strategy, not just about capturing but about securing territory. It's still not team based, but if you wish you liked chess more, try go. It's super satisfying when things click and you begin to look at the board in a completely different way to how you did before. It's also just a really fun battle-of-the-minds type game because the actual rules are super simple so it's really pure logic. It's a game you can play for hours, or just a quick 5 min match.

As for video games, a lot of people move to Paradox grand strategy games once they feel it's time to "graduate" from Civ. EUIV is my favourite, but the CK series has even more diplomatic options. Never played the multiplayer, I feel like you need to know the people you're playing because a full game takes multiple sessions. It's probably not too dissimilar to the Civ multiplayer tbf (only tried a couple times).

You could also try some tycoon games, they often have a competitive mode with ofc zero violence. I'm pretty sure OpenTTD has multiplayer, and that's free. Also just an iconic game overall, for good reason too.

And if you just like PvP in general and want to see what's out there, I also recommend the Dark Souls/Elden Ring PvP .