The PS2 uses a different video clock than the PSX, at 54 MHz rather than the ~53 MHz used by the PSX. This means that optimized timings are quite different between the two.
The target optimized sample rate per line for the PS2 regardless of whether you’re playing PS2 or PSX games should be 858 (NTSC) or 864 (PAL) for 640 pixel wide games, 686.4 (NTSC) or 691.2 (PAL) for 512 pixel wide games, and 490.3 (NTSC) or 493.7 (PAL) for 384/368 pixel wide games. In the optimized modes for 320 and 256 pixel games the sample rate should be set to half that of 640 and 512 respectively.
The OSSC oversamples 256 and 320 pixel optimized modes at 2x and also does its best to find a multiple of the fractional rates resulting in an integer number of samples per line, discard samples to recover the desired resolution, and repeat the pixels to maintain the aspect ratio the best it can. It’s often not perfect.
If you can use a higher line multiplication factor with your display and the OSSC set to 4:3 Generic mode, you’ll get a picture that’s oversampled to match the vertical scaling factor as closely as possible. Given that the PS2 has rather high video bandwidth, this can still give a sharp picture and be the best compromise across in-game resolutions, especially in games that switch resolutions between gameplay and menus.