My feel is that the P1 is a great starter turntable at a very good price, but the RB110 arm with fixed bias/anti-skating is limiting as it can make it hard to try alternative cartridges which might need different bias.
The P2 has the RB220 arm, but until late-ish in 2020 that also had no bias control. Current versions do have it, so if you buy one be sure it's the new one - I wouldn't be at all surprised if even some dealers still have old models. I would never buy an arm with fixed bias, and I think Rega made a stupid design decision with the early RB220, but thankfully it's rectified now.
But the general thought seems to be that the next best bang-for-the-buck model up the scale, after the P1, is the P3. It has an RB330 arm, heavier platter, bracing on the plinth (I retro-fitted a brace to my old P3 and I was surprised that it made a difference). It's also compatible with the Neo power supply for a possible future upgrade - that's another upgrade I've done, and again I was pleased with the improvement.
And yes, I think it would pair nicely with the IO, which is an excellent little amp. I suggest you get a Rega dealer to give you a demo of the P2 and P3 with an IO.
Or, as acgingersnaps suggests, try a cartridge upgrade as an intermediate step. I agree it could make a noticeable difference. If you get a decent cartridge that would also work well on a Rega, you could migrate it later if you do choose that path. I wouldn't say, though, that a turntable upgrade is necessarily marginal. It will probably make marginal tonal difference if any (which is where the room/speaker thing comes in big), but it can significantly improve resolution and imaging. Some people are driven by tonality, others (like me) chase resolution and transparency.