the interchange with merchants is not not something I'm accustomed to - this seems to be a big part of the experience
I'm not a huge fan of shopping but it can be valuable time. This sort of play is what I call "low melodrama" play and it's about slice of life, character development, and chances to develop relationships between PCs and and between PCs and NPCs to get payoffs later on. I think the secret here is not to focus on the shopping and whether or not as a DM I do focus on the shopping or encourage players to handwave through it depends on whether or not I think there is a bigger goal than just getting tools to overcome challenges.
A lot of players can't lean into low melodrama. It's one of the rarer skills and rarer aesthetics of play, but CR does it really well. My advice to you as a player or GM is to think about what you want to accomplish in a scene at a meta level and figure out a way to start that using the GM as a sounding board and if possible bringing other PCs into the scene.
I'll give you an example of a low melodrama payoff in one of my games to show why I don't just ignore it as a process of play. In one campaign a PC priest had been charged to spread the cult into a new city. There was no temple in the city and he was living in a small apartment near the temple district where a lot of the other minor figures in the religious life of the city dwelled. And I made a point of introducing his neighbors - a seamstress that repaired and sowed ceremonial robes, one of the other PCs who was a lay brother at temple of the goddess of beauty who worked basically as a stagehand, and family that were undertakers responsible for burying the dead and assisting the priests so that you wouldn't get nasty accidental undead (or at least, that they'd stay buried if you did). We spent just a little time between adventures where he'd talk with his neighbors.
What he didn't know is that the neighbor who was an undertaker was actually the BBEG that they had spent the first two years of the campaign real time chasing and trying to discover. When they figured that out, pay off.
So instead of thinking of it as a shopping expedition, think of it as time you as PC are allowed to create exposition. Talk to an NPC about who your character is. Use that get to know the NPC time to define your character, bring up your backstory and create opportunity for the DM to get you involved in something. If the DM really is good, then he's going to recognize when the pacing is getting too slow and move things along.
the depth-of-character is really impressive, but again, I'm simply not accustomed to it - the group is "really in character" at the table
This is hard. And as used to doing it as a GM as I am, leaning into it and staying in character as a player is still a skill I have to cultivate. In fact, because I've been GMing so long, when I play I feel really rusty as a player and "out of shape" and like I'm not as good of a player as I used to be, which is disheartening and only makes it harder to play well.
But you can tell the skill of a group of players by how much interplay they do with each other in character. And I'm sincere about that, in that groups that are usually good at that are also usually really good at tactical problem solving, puzzle solving, and everything else because you don't cultivate that hardest of skills without doing a pretty good job of also cultivating the easier ones along the way. Everyone has different strengths and maybe you'll never be a great actor, but if you can throw out RP and entertain other people at the table, you are probably a pretty good play all-around.
[*]the killing move, "how do you want to do this" is something new to me
There is a proposition loop in gaming that runs something like this:
a) Propose to do something to change the game fiction.
b) If that something is doubtful, test your fortune.
c) Narrate how your success or failure altered the game fiction.
d) Repeat.
Steps 'a' and 'c' allow someone at the table to narrate what will happen or what has happened. The more skilled the player, the more they can partake in that narration. Most novices leave it up to the GM, and it can be difficult in some systems to delegate 'c' fully to a player because the player has limited information. What your GM is doing is trying to encourage you to take more control of the narrative, and having dropped a foe is a great time to do this because it's a moment when you have complete information. You know that the foe just died so you know the parameters you are allowed to narrate. You get a moment to narrate your awesomeness and add to the story. Essentially you get to wear the GM hat for a moment and tell the group what happened. Mercer doesn't always do that, and maybe your GM doesn't either, but it's cool thing. And as a GM, I like it when players can lean into that sort of thing because a lot of the times I feel uncomfortable as a GM telling a player what they do. So like when you do have full information, go ahead and narrate your success or failure and don't make the GM decide what your character does during their moment of success or failure. If you fall down the stairs, say how you do it. If you get the killing blow, say how you do that too.
the mechanics of the game seem to be less important than the story of the game
They always were. And the reasons for that are straight-foward. First, the mechanics exist for the sake of the story. And secondly, the mechanics are never complete and so you always have to bend them to cover situations that can come up outside the clear cut rules. You should never feel confined to making only rules propositions. It may be true that your character can't be awesome at everything - there is often a problem where the rule of cool gets misapplied to mean you can succeed at everything - but lean into whatever heroic things your character can do.