The balance of seats in the Senate

>" The balance of seats in the Senate "

Do you mean the House? I think the Senate would still have 2 senators per state, and state-level electoral results are unlikely to change if an alienated minority from one state secedes, in favor of joining a more (politically) similar state.

I'd imagine a common theme would be for red counties in deep blue states to leave and join their light blue neighbors, which may shift them red. (Or vice versa.)

For example if upstate NY joined Pennsylvania, then the D senator from PA would very likely lose. Or if (Republican-leaning) inland California joined Nevada, then Nevada would probably tip red. Or maybe (heavily blue) Jacksonville and Gainesville get fed up with DeSantis, and leave Florida for Georgia, cementing GA as a solid blue state.

what makes you think there light blue neighbor would have them?

What happens when you get down to the last county and they also want to join another state?

If there were a one-county state, it would benefit from so much graft that they'd never join anyone else. Imagine having two senators, one congressman, and three electoral votes, all in one county! Every presidential candidate would stop there and promise them the moon!

I imagine the first time a county successfully split to join another state, a lot of states would just abolish counties altogether. Then everyone can be in a one-county state...

Rhode Island is close enough and mostly doesn't get paid much attention.