Hii!! i am so sorry this reply is so late, to make up for it, i tried to add every single fic i could find that you might like!

1) found family trope/team as family, mamahwa (to the team):

• the days i prayed by tremulousbird
  one of the best omegraverse fics ive ever read, elli rlly nails the "pack dynamic" and "theyre a family" feel, the bonding moments between hwa and the teezers are the best

• fire & rain by inexperienceandconfused8
  after their ship crashed, sh and 7 other survivors have to learn how to live on a deserted island. this one is peak found family, anything of this author is peak found family/sh mothering the team, but this one especially rlly feels like sh and hj adopted everyone else.

• seafoam and ocean winds by squishh
  pirate au, sh is secretly half-harpy, I technically already recced this fic in the pirate thread but im putting it here again bc!!! i absolutely love how protective sh is of his members in this!!! ur looking for found family well you will find it here!!!

• do you even know how to stream? by wonymph
  ateez are streamers all living in the same house, fans are curious about the mysterious "hwa-hyung" who never shows himself
  sh is the ultimate mom of the group and he is the sweetest ever and this fic is literally one of my absolute favourites, its a must read trust meeeeee, its just pure fluff and everyone adores hwa

• A match made in heaven by velvet_hwa
  omegaverse, bridgerton au, ateez are family in the literal sense of sh being yunwoo's mother and hj being jonggi's father
  i LOVE the family dynamics in this one, and im a sucker for royalty aus with a bit of enemies to lovers so ofc i had to add it to the list

2) kidfic (mamahwa to his own kids):

• Love but backwards by itsLivvvy
  omegaverse, hj asks hwa to be his pretend mate and have his children, somewhere along the way it stops being pretend.
  The entire series is amazing!!! i rlly love hwa's relationship to the rest of the teezers, they all rlly care ab him, honestly all of liv's work tends to have a lot of found family in it!!

• life finds a way by Im_Moon_Wang
  omegaverse, sh wants to be a parent badly, but hes told that he's unable to conceive. He decides to adopt instead, but then after a one night stand (with hj) he ends up pregnant and decides to raise both of his kids by himself
  rlly cute fic!!!! it was rlly sweet with sh being an adorable mama, and hj trying his damn hardest to be a father despite sh's claims of being fine on his own

• I'll be your star by meanttowooyu (baeknfectionery)
  omegaverse, a one night stand leads to sh getting pregnant. after six years, hj finds out he has a daughter.
  i love sh so much and i love the teezers so much and i love how every teezer that meets sh immediately adopts him, honestly this is as much found family as it is a kidfic

• the spaces in between by matzness
  accidental baby acquisition, co parents mtz
  basically enemies to coparents to friends to lovers, while they both deal with the grief of losing their friends and raising the newly orphaned daughter together
  its one of those kidfics where you can rlly feel what it means to be a parent and i mean that in the best way possible, mtz basically fall in love by being the one person they can trust to rely on in times of need and honestly!!!! the yearn of it all is what makes it worth it!!!

thats all i have for now, i had a lunahwa fic i wanted to rec but for the life of me i couldnt find it so,, either i didnt bookmark it or its gone :')
still i hope u enjoy these!!! i have a lot of found family fics if you do need more as well!!!
if you cant find any of these fics and need a direct link pls let me know and I'll post it for u!!