I think it's easier to get around to this by directing you to another question.
Why was Lord Gendry Baratheon, the Rejected there?
He was a bastard, so not normally recognized as a legitimate heir. He wouldn't even hold the Baratheon name normally. The only person who had recognized him as the legitimate holder of the Stormlands, and gave him the name of Baratheon, was Daenerys.
As such the take away seems to be:
Anyone recognized or appointed as a Lord or Lady by Daenerys is legitimately so.
Certainly the Unsullied would have an interest in this, as their fanatical devotion to Daenerys would make them want her works and proclamations to carry through. As was noted by Varys, Gendry would be a loyal vassal thanks to the act, rather than a liability. So we can probably be safe to assume even more:
All political (non-war) acts and decrees made by Dany remain valid.
This may have been a simple necessity in negotiating the meeting with Grey Worm and the Unsullied, who had Jon (and Tyrion) as prisoner.
Back to Sam
We never see Daenerys specifically declare that Sam is now the Lord and head of his house. There are some indications that she presumed this. After killing Sam's father and brother, everyone's reaction seems to be that Sam is now the (male) heir.
Furthermore, when Daenerys meets Sam for the first time and asks him if there is anything she can do for him, he requests a pardon. He only specifically mentions his theft of the books and the sword. We do not see Daenerys (or anyone at all) make any further mention of this. But it seems implicit from the scene that anything he requested that was within her power would be granted (implicitly immediately, if so). Ser Jorah accompanied her for this encounter, so others would have known. And she may have simply given a rather more general pardon, or others (such as Grey Worm, hearing of it second hand) may have interpreted it as such.
The pardon itself was meant to reward him for his major contributions towards The Great War. Much as Jon tells Arya that no one would seriously have the stones to tell her she's not allowed at the Wall, thanks to being the one who slew the Night King, it may well be the case that Sam's important contribution is also well-known. So much so that no one would really have the stones to try to punish a man so important to saving all of Westeros.
As such it seems plausible to suppose that:
Daenerys likely pardoned Sam for his crimes. And popular opinion would have been high enough to make it politically unwise to punish him regardless.
By the previous part, a pardon, even implicit, by Dany may have been deemed valid. As such there was nothing further for anyone to do. But even if you don't like stretching what we saw that much, we do have indications that the second part would be valid.
And as a bonus back-up possibility, it seems the Night's Watch, or whatever is left of it, isn't too keen on rigidly enforcing the old oath anyway. The ending seems to suggest that they just let Jon waltz off with the Free Folk to live unfettered, north of the Wall. As such anyone who contacted the Night's Watch concerning whether they had an oathbreaker on their hands who needed to be duly punished, may have simply been told "nope."
Really the overarching idea here seems to be that everyone has had bigger problems to deal with, and Sam's oath and theft were irrelevant trifles in comparison, and as such duly ignored while they dealt with the big fish. Just as no one evidently tried to contest Gendry's lordship: there were bigger problems to deal with, and if he was dealing with the problems of the Stormlands rather than them then all the better.