Let's just start off by saying, all critiques below, aside... I enjoyed this, and look forward to more. It's a fun idea for a combination, author, and I hope you continue it. So, that said..
Biggest critique: the author doesn't strike me as as being SUPER thorough with character details or to seem to know the material of either the Addams Family or Harry Potter extremely well.
Character detail issue: as an example that pops up a few times in different ways, in the early chapters the character talks about muggle studies and it's clear that they're pureblood and don't know muggle society. ... But within a chapter ends up quoting a famous American Muggle author from memory, which is just layers of odd choices for a pureblood wizard. Not only is he reading muggle authors, he reads them enough to be able to quote _poignantly_ on topic, all while going to Wizard school in Scotland and having a full academic schedule as he, I assume, prepares for his Newts or Owls, or whatever year he's supposed to be.
Second issue (as an example of not knowing the settings): Grandmama (the Grandma in the stories,) is literally called a 'witch' or fortune teller; has a big warty nose, brews from a pot, spouts curses and hexes at people, uses voodoo, etc. It's not a thing that shows up in Wednesday (IIRC) YET, but I wouldn't be surprised--AT ALL--if magic of some variety shows up a bit more in the next season. It's not at the level of HP, so MC would have a huge leg up still, but acting like he's some unique unicorn is just weird.
Lastly.. he's a Slytherin (cunning, ambitious), and not stupid, yet he apparently can't keep from spilling the beans about his coming from another world through more that ONE conversation with Weems, or ONE day of knowing Wednesday. Like, I don't care that he spilled, but he apparently does, and just can't keep a secret to save his life?