The letter panel looks like a quest board and is not one. Nothing in it is tracked, nothing appears in the quest log, and no letter ever schedules anything at the other person's end.
Asking to meet (会面) does not ask anyone anything. MailView.OnClickSendVisit writes your letter and
then immediately composes the reply itself:
There is no meeting, no marker, and nothing to go and do. A brush-off is not a cooldown either: send again later and, if that character is active by then, you get the real answer.
The 索要礼物 letter with an 接受 button is settled in the panel, not in the world:
It never becomes a tracked task, so there is nothing to look for in the quest log — come back and press accept when you have the item.
It pays no relationship. The accept path removes the items and posts letters, and does not touch 好感 or 情分. Handing the same item over in person does: the gift panel converts an item into both, scaled by its quality, its level and that character's taste for it, and shows you the numbers before you confirm. Mailing away an item that could have been a gift is throwing it away.
MailManager.SetMailFinish fires a "letter finished" trigger, and the letter-condition table can hang
new letters off that. So closing letters advances the correspondence — that is the mechanical payoff,
and it is invisible.
When a gift letter (送礼) arrives, its items are created directly in your inventory. There is no collect button and nothing to click; the letter is the receipt. If someone "owes you a drink", check your bag rather than waiting for a prompt — and note that the promise itself is flavour text drawn from a random pool, not a debt the game records.