Russia’s inability to conquer any of its neighbors is irrelevant. The possibility of them even attempting is unacceptable if you share a border with Russia. Sure, maybe Putin can’t hope to depose your government, but the destruction and deaths before his failure are still a horrifying reality that’ll take years, possibly decades, to recover from.
As for why Sweden felt the need to join, despite not having a single meter of border with Russia, it’s because Finland felt the need to join. The two countries are tightly bound and do not want to end up on the opposite sides of a war. Now they’re much less likely to.
The show made a fair few changes from the books, mostly for the better. Off the top of my head, Avasarala and Draper are introduced earlier in the show, Drummer got the consolidated stories of several other side characters and Elvi Okoye’s and Ashford’s personalities were significantly changed. IMO, Show Ashford is a much more interesting character than Book Ashford. In addition, the season 6 side plot with the kids is told much later in the books.