Google's John Mueller said there isn't an added delay in Google Search Console reporting for those who have many verified sites in their Search Console accounts. The delays are not specific to the number of sites you have verified but just generic delays in Search Console.
Gregory asked, "The update of #GSC could be delayed if we have too many sites in the same account?" John Mueller of Google replied on Twitter saying "Nope."
Here are those tweets:
Nope
— ⛰ johnmu is not a cat ⛰ (@JohnMu) October 14, 2022
There are a number of pipelines that lead up to the data being in search console. Sometimes one or more of them will be a bit delayed or "clogged", and search console just makes that more visible. It's just for reporting though.
— ⛰ johnmu is not a cat ⛰ (@JohnMu) October 14, 2022
I've never seen this question, so figured I'd cover it because it is new...
Forum discussion at Twitter.
Note: This was pre-written and scheduled to be posted today, I am currently offline for Simchat Torah.