Agreed. So much about Raffi's backstory doesn't stand up to scrutiny. Why would she have been kicked out of Starfleet? Just for supporting Picard? I know the show is positioning Starfleet as a quasi-antagonist who had "lost its way", but I can't believe they would "fire" an experienced officer just because her CO resigned in protest.
That feels ridiculously petty and vindictive and I wouldn't buy that as being realistic in a 21st Century organization (without additional justification, let alone Starfleet of the 24th.
Nor do I buy that Jean-Luc would be so callous as to completely cut Raffi out of his life and quite literally never speak to her for all those intervening years. That's just....some really bad writing there and wildly out of character.
I think it's that Raffi lost her purpose and her career, which seemed to mean everything to her and is severely depressed as a result. A few years ago I lost a job that I loved and that i felt gave me purpose and had a breakdown. It's taken me about two years to recover from. Some people aren't so lucky and they let their vices that they use to cope overcome them. I can also see how a post-scarcity society where everything is given to you could be bad for a person potentially suffering from a mental illness. You don't have to pay rent, buy food, buy clothes, so what is the point in trying? Where is the impetus to get you back on your feet and rebuild your life?
I also got the vibe that Raffi may have already been in Starfleets bad graces and Picard was protecting her. With Picard out of the way, someone in Starfleet HR may have seen an opportunity to get rid of a 'non-team player'.
As for why Picard never spoke to Raffi, it may have been something that 2364 - 2379 Picard wouldn't have done, but it may have been something a Picard who has lost his faith in the organisation he has given his life to may do. 2399 Picard is a different man to the one we know, in fact I don't think he even knows himself at the moment.