A BuzzFeed article from 2015 with a poll in it:

16% with over 1,000. I’d say 1,000 is a good cut-off line for uh yeah this is a problem. If you’re in the hundreds, that might be because you’re just back from vacation or you’ve neglected it for a little too long. But hope is not lost, you can probably knock through it fairly quickly if you focus on it.

Plus, you can make it into an opportunity. Focused time on whacking down a huge inbox means you’re also probably in the mood to be unsubscribing from things and changing notification settings so this situation is less likely to happen again at this scale.

Over 1,000 though, it might be an unreasonable ask of your time. You’re probably in a situation where you want to scan scan scan, find anything that looks obviously super important and save, then declare bankruptcy on the rest and archive.