I’ve thought about if we’ve seen Jimmy in BB, too. The two moments that come to mind are in his last scene when he finally walks away from Walt and around the time when Mike threatened him on the whereabouts of Jesse and that shook him up.
The only thing that doesn't really carry over between the shows, in my view, is Jimmy and Mike’s relationship being much deeper that it seems on the original show. Considering what we now know about what they’ve been through together (particularly in recent episodes), Saul not having any reaction in the desert when Jesse outs Walt as having killed Mike is a bit weird. Though you can find reasons to explain that, so it’s not a big deal.