Ina's name is definitely a bit of homage to our priestess, but that's as far as I went - anything more and it starts lurching too close to plagiarism. So no abyssal relation with her, and she won't be a priestess of the old ones.
Other characters may end up closer to that niche though, I do think Hololive Ina's design is fantastic and something along those lines could work in the setting! Just not obviously Ina.
Abyssal will get its own, hopefully unique stuff - though the Lovecraftian vibes aren't too subtle I admit!