I have a 2TB SATA HDD in my PS2 fat. AFAIK that's still the maximum storage size possible with the FMCB/wLaunchELF software. I believe that an unmodded original network adapter should be able to take up to a 512MB IDE drive, but I'd have to double-check that.

I used to use a third-party "network adapter" (they usually don't have Ethernet, just an HDD connector) with SATA support, which still works fine (it seems like most brands stopped working properly after a certain homebrew software version), but later I bought an official adapter (IDE/PATA) and a SATA conversion kit (a kit specific to the PS2 network adapter, not a standard IDE-SATA converter, which sometimes work with the PS2 and sometimes don't) so I could try network stuff.

I don't think it was worth it, but these days it's probably the way to go since there no longer seems to be any way of telling the non-working aftermarket adaptors from the working ones; the companies making the bad ones just started putting the brand name of the one still working adapter on their products.