OP, this, this, 100 times this.

Currently, it sounds like they are settling for the worst option, which is to not implement backgrounds in dialogue at all. It's great and all that the system will acknowledge it for whatever checks, but if you can never talk about it, it feels less present/real/important which makes the character feel less present, real, and important.

The less ideal way to go about it would be less detail, keep it vague but still KEEP IT. If the problem of the Folk Hero tag in conversation is that it begs the question, "In what way are you a folk hero?" you could simply have the details not included but the outline there. You could say something like, "I'm kind of a big deal" / "I've handled this sort of rescue situation before" / "I do this all the time" and an NPC could reply, "Oh, I've heard of you, some hero, huh?" type of thing. Obviously with better writing. It's vague, but it's still in some small way acknowledged and leaves the player to fill in the rest.

The dropdown menu at character creation would be a solid way to implement it without needing additional cutscene-style moments and/or additional writing specifically to clear it all up, and would allow for more specific tags for checks+dialogue throughout the game from the get-go. That being said, DA:I had a conversation or two fairly early on that was designed to let you specify what your past was like and your options there were remembered for future references (not a lot of references, unfortunately), and I think the idea of having a thoughtful camp moment or dream sequence style to determine specifics is similar and would be really clever if the capability is there to have responses remembered for future reference in conversation and system checks.

If the capability is NOT there to remember responses (which would strike me as odd) then and only then can I understand the hesitance and the decision to just drop it entirely from conversation dialogues and focus on race and class checks only.

The concern is that a custom character does feel like a watered down Origin character, or did in DOS2. Previously we were told that would not be the case with BG3, but the stream stated things have changed since what they were originally trying to do. Origin characters may have the same tags as a custom character, but more of their details can be acknowledged in the game. For example, the camp scene in which Astarion contemplates events: he was seducing a young noble, luring him to his Master -- he can think of things related to his specific past, the lack of sun and his Master's temper and so on.

Will a custom character have that moment? Would it be that specific? How could it possibly be, if their background isn't acknowledged to the same degree? Maybe some people would be fine playing that out in their head, essentially pretending throughout the entirety of the game that who they have been is being acknowledged, but for the game design and content itself, that suggestion is severely lacking.