Nodding along to all of this.
As a clarification: I considered "embarrassed" a good general word. Maybe a more general word is "uncomfortable", but I don't seem to mean by "embarrassed" what I seems like maybe you think I mean? Which is to say— I agree! He doesn't like the assumptions being made about why he did it, including the assumption that it was lust. I characterize his feelings about being misread (and also teased while being misread) as embarrassment (which also very often co-occurs with anger, which I also agree is happening here). I do think there's something about everybody knowing about it that is also upsetting him, but probably wouldn't if they weren't making the assumptions about his motives that they were (or if it hadn't gone the way that it did). Obviously, people are welcome to use different descriptors to dig into the mess of it more.
It's actually really interesting and almost counterintuitive that he just says it outright and that it's important to him that they all understand this was his motivation. At this point he’s not even showing shame about the idea.
Yes! I do also think this is Grace-connected. He slept, specifically, with a woman who his wife thought wanted to get in his pants. That was what Grace was arguing with him about moments before she died, and that only adds insult to injury in terms of being the windower who now everyone is saying "haha you slept with a duchess" As if he wanted to do it just for the hell of it, and that bothers him in part because his grief is not seen (and imo we get Tommy feeling unsupported and misunderstood in his grief in 3x06 too when he says Lizzie was the only person who helped him). It's what—an episode before this that he grabs Tatiana by the throat for suggesting he didn't care about Grace after all? And we get that moment where he looks up at Grace's portrait before convincing himself to track Tatiana down again.
There's a big separation between offering up someone else (especially a woman who is 'impure' already, as he assumes Grace is in s1 and as Lizzie is) and offering up yourself, especially as a cishet man, and I'm always interested in people's thoughts about where that comes from in Tommy. Because it doesn't seem like a new idea to him at all even in season 1 -- "Everyone's a whore, Grace." Again, not something his brothers would say about themselves.
I do think this is where people's "Tommy may have been previously sexually abused" (or maybe even more specifically "Tommy may have prostituted himself as a kid") headcanons really work well, with Tommy also characterizing himself as "impure" because of that.
Setting those headcanons aside, we also see Tommy's general ways of processing/coping with trauma tends to diverge from his family, though (to the point his family often doesn't really understand him). Trauma changed not only how he reacts to things but his whole worldview, and we could suggest that for Tommy specifically, something about spending the war feeling like a weapon and feeling disposable (and maybe even how that process continues through section D) makes Tommy more likely to see himself as an object who is suitable to be used in this way. In season 2 in particular, the Irish business is affecting Tommy pretty specifically, and he's keeping everybody else out of it.
It did just occur to me: While I think arranging John's marriage is a bit different, maybe it is worth thinking about that fitting here too in a way. Maybe Tommy putting himself, Lizzie, and Grace in this separate category isn't as clear cut? Hm. (There's also the scene where John and Arthur have to disrobe at the Petrovna house... maybe there's something even more different going on there too though. It's... interesting).
The context around Tatiana's "offering" sex is that she's been ordered to do so by her aunt and uncle as part of their plans -- she's basically just as coerced as Tommy is in s6 with Mitford, probably with fewer options to refuse. So it becomes very interesting to consider in terms of "offering sex as a means of establishing trust and gaining information."
This is in a large part why Tatiana is so transparent about it in my opinion—because it isn't her own idea—it's her family's practice, so she doesn't care about subtlety, and that's SO interesting imo.
So this first instance where Tommy is directly exchanging sex for trust/information has elements of coercion on both sides.
Yeah yeah yeah it's soooo *chin in hands*.