Apparently there is no limit.
The thumbnail of the following video shows
2032: How To Get Rid of The Number On The YouTube Tab ll Remove the number on Youtube Tab llAyseeTech&tips
I found the above video by googling
youtube shows 99+ in tab. I used 99+` because I was thinking that it might be the bigger number that could be displayed in the browser tab next to the page title. Actually at some point in time I was correct, as according to How To Get Rid Of The Number On The YouTube Tab, a post dated as 2017 says:
> If you have a lot of them, the number badge will read 99+.
To double check I suggest you to do something similar, google and look for posts about the number shown by Youtube in the browser tab, look at the Google Images, at Youtube videos, among other content.
Also it might be a good idea to look at specialized communities about web scraping.
Actually there should be a limit set to assure that Youtube run smootly and doesn't cause problems to end-users. I don't think that this specific limit is publicly disclosed, if could change at any time.