I have the Framework, and I haven't noticed anything off with the display's "in-between" resolution.

Same here. I’m using it with Fedora and wayland’s 150% scaing works perfectly nowadays.

I haven't tried Fedora lately, but I had trouble with fractional scaling on Ubuntu, especially when combined with X11 apps. Ultimately this was part of what (but not the only thing that) drove me to switch to running Windows 10 on my Framework, which handles the laptop's screen resolution very well.

Everything appears sharp? I had had issues with Ubuntu and fractional scaling a while back with blur, but I'd elated if this is something that's been worked out in wayland. Come to think of it, wayland may have been fine, and xorg was the issue. I'm forgetting at the moment.

I have one too, using it with Linux.

I'm using it with fractional scaling at 175% and I notice that it's less sharp than with either 100% and 200%.

I use pop!_os 22.04 beta with wayland and fractional scaling 125%. Some software needs to be told to use wayland stuff, but otherwise it is sharp as a tack.

For instance: MOZ_ENABLE_WAYLAND=1 firefox