Sorry for the long post! While I'm going back and forth about the direct fix, as far I can tell without getting too optimistic, my sound/combat soundest/banter is now working 100% as intended - with the joys of RNG and all. The banter can still be sporadic, but it's happening far more organically before. No matter which party combo I put together, everyone will eventually talk to each other - this was very much not happening previously. There are no longer party members who are dead silent - looking at you, Vivienne and Varric! (Vivienne and Cole had interactive banter, it was my first one. Finally some banter out of Cass/Dorian, too.) There's a definite, noticeable difference. I hope it lasts.
I'm not entirely sure what the fix is, but the most important thing I've noticed in correlation, is that my journal is now working as intended. The quests are auto-completing properly without intervention. I still check the journal constantly, but it's now very, very rare a quest hasn't completed, and I need to manually trigger it. (I haven't even bothered with the codex.) While this has all happened post-patch, what has also happened is that I've been trying to go back and clean up as many quests as I can pre-Act 2 main quests. The Hinterlands/Storm Coast/Fallow Mire only have about one or two quests left. I'm nearly finished with the Emerald Graves and Crestwood. (Over levelled, I know.) I've barely triggered any quests in the Exalted Plains/Hissing Wastes/Western Approach, and what I have started, I've mostly completed.
I would have thought the patch fixed it, but for the first day of playing after the patch installed (4 hrs?) I was getting no banter whatsoever. It was only the day after that when I started cleaning up quests in the Emerald Graves that finally I had banter. I think I had about eight or nine in the space of about 4hrs? I went to Crestwood after that, and noticed the journal was now completing quests properly. All I can stipulate is that the game has less to keep track of, and with resources freed up from keeping track of an MMO-tier amount of quests, it's easier to keep track of everything else. Music and combat soundsets are there 100% of the time, no issues at all.
re: banter and combat, I've noticed that I now always get banter after closing a rift. For the one time I didn't, I had some ambient banter instead. Sub-areas inside regions also seem to help, especially after they've been cleared of enemies. (There's a mini-castle with its own loading screen early into the Western Approach; the Storm Coast has a large enough unlockable sub-region that I'm assuming the majority of the Storm Coast would not need to be loaded at the same time. I think I had three party banters trigger whilst trying to find a bloody key in there.)
The real test will be the dead zone that is the Western Approach, or the Exalted Plains.
Even with it working as intend, the RNG gods can be pretty absurd. I've had three occasions where I've walked the up and down the length of the map of the Hinterlands with no banter despite no combat or NPCs (areas cleared out), and yet sometimes I'll be going from combat to combat, and banter will trigger. Sometimes just as I start combat! The funniest issue I had was that banter triggered right when I swapped Blackwall from the party, so Dorian had a prolonged one-sided conversation with himself. I've also had banter repeat itself for the first time, which was a bug I'd never gotten previously.
For those whose sound/banter is now working, is your journal quest-tracking working correctly, too? Again, I don't know if the patch fixed the journal, or clearing out a lot of quests before adding more that has helped. Bolding for understandable TL;DR! - Either way, the journal/quests auto-completing without intervention and party banter/sound firing properly seems to going hand-in-hand 100% in my game.