How long can they actually stay below the surface in practice though? I'm guessing water is filtered on the vessel, but food must be re-supplied constantly I'm again guessing? Maybe they do it like airplanes refuel in the air, rendevouz with another submarine and somehow transfer the resources for food making between then? Probably read too much Tom Clancy...

https://en.wikipedia.org/wiki/HMS_Warspite_(S103)

Seems like the record is 111 days submerged.

Nuclear Subs are typically pretty big so they can probably bring enough food to last for the entire time without resupply.

3 months. There's an episode by smarter everyday about it