So if Bilbo was saying "He was... He was my..." is because of -cultural differences,- wouldn't that kinda imply that Bilbo's acknowledging that there was definitely a thing going on between them, but he didn't know what would be the most understandable word for it? Like... they may have been courting by Hobbit standards, but were they by Dwarf standards? Was that even a TALK that he and Thorin had?? A serious, sit-down, "we wanna marry but how do we go about it" kind of talk???
“…wouldn’t that kinda imply that Bilbo’s acknowledging that there was definitely a thing going on between them, but he didn’t know what would be the most understandable word for it?”
YES, i think so. unfortunately, i don’t think there was much discussion between Bilbo and Thorin about what was between them. if there was a sexual relationship i headcanon that it was of the “both parties think the other party is just here for the physical” variety. i think it’s just as likely though that they never had a sexual relationship, though i believe Thorin at least entertained romantic feelings for Bilbo before they reached the mountain. whether he acted on this romantic feelings is hard to say. there was no time for them to talk about them, not with everything else that was going on, and the fact that after entering the mountain, Thorin went mad.
“…they may have been courting by Hobbit standards, but were they by Dwarf standards?”
I don’t think they were courting by hobbit standards, but I DO think the mithril shirt was a courting gift, by dwarf standards. Thorin’s affection/romantic feelings for Bilbo were brought front and center by the dragon sickness; that’s not to say that Thorin considered Bilbo part of the hoard, but that the sickness lowered his inhibitions, clouded his judgment, and flooded him with delusions of grandeur - Thorin literally thought he and Bilbo were going to rule Erebor together, and that everything in the mountain was as much Bilbo’s as his. Thorin placed them on equal planes, both figuratively and literally (the throne dias).
The sickness stripped Thorin of his ability to reason, to think rationally and critically. if Thorin held a secret desire in his heart for Bilbo to remain in Erebor after the quest, by his side as his consort, then the sickness allowed him to believe he had already achieved this/could achieve it without even consulting with Bilbo rationally on the subject. again, not to imply that the sickness made Thorin possessive of Bilbo - we saw no evidence for this. But his illness did make him act in ways that he never would otherwise, including treating Bilbo as if they had already decided his place was at Thorin’s side, elevated above the dwarves in a position of honor and authority.
Bilbo, on the other hand, didn’t realize the extent of Thorin’s feelings for him until Raven Hill. he might have guessed at it, he might have wondered, but i don’t believe he allowed himself to confront it until after Thorin died. Thorin’s behavior in the mountain would have only been strange ,erratic, and worrying for Bilbo - but he’s no fool, he would have wondered why Thorin didn’t order him to search for the Arkenstone, why Thorin never suspected he had taken it, why Thorin doubted all his kin, but never Bilbo. and i don’t believe Bilbo realized he loved Thorin romantically until Thorin was dying/died.
With all of that, with everything that was there but unsaid, all that could have happened between them but never did, Bilbo struggled to classify his relationship with Thorin. More than a friend, but not in anything other than feelings and unspoken (but understood) affection. Thorin was his… his what? What’s Bilbo supposed to say about someone he loved, who loved him, that died too soon for them to acknowledge their mutual feelings.