I would imagine the estate has something like 30 days to get belongings before things are considered abandoned.
That's probably not correct.
In the absence of evidence to the contrary, a person is presumed to own that which is in their possession.
That he inherited the house makes an even stronger presumption that he also inherited the contents of the home and also raises the presumption that the deceased intended it that way when executing the TOD.
Your assertion that the lack of revocation of the TOD was unintentional is biased and self serving. There's no evidence of that.
To be entitled to anything in the house (rebut the presumption) one would have to provide evidence (not just say so) that items where the property of the deceased.
A bequest in the will of any specific items to somebody else would, of course, be strong evidence that the owner of the house was not entitled to those items.
Everything else, I think, would belong to the owner of the house unless he was gracious enough to allow removal.
I admit I have no legal citations for the above, just a reality check. If the homeowner says "It's all mine, prove that it's not" then what do you do?