Linux Mint's Cinnamon desktop has beta support for 1.25x 1.5x scaling... it's on the right track but has ways to go - the menus don't adjust, there's work to be done for sure.
I wish I had the skills and time to help out, but for now, all I can do is point out the irregularities, I'm afraid.
Try a smaller 4k monitor, no bigger than 24":
Cinnamon has a more gradual setting in beta, but the implementation isn't complete yet - the menus don't adjust well - I'm guessing there are some other GTK related quirks to iron out.
1) The display preferences panel did not know about my custom backing framebuffer and kept re-setting it to match the native resolution on each click (could be resolved by careful ordering of operations)
2) The mouse cursor became tiny (could be set to bigger sizes, although it looked like you are picking an unreasonably huge mouse size on the control panel)
3) Couldn't break out of the original 4k bounds with the mouse
...and that's were I left it last time.
Every month I read here that it can’t be done.
This results in a 2560×1440 effective resolution with a bit of blurriness that is acceptable, compared to "native 200%" scaling that makes the controls a bit too large to my liking, or "native 150%" scaling that is hidden behind some "trust me, you don't want to see this" language/button in GNOME.
Things do seem to be slower when it is switched on, which is not the case with the 200% and 100% settings.
This size is very difficult to find these days, presumably because people don’t understand this. Or hardware co. mgmt didn’t.
TL;DR A 4k monitor should be the same size as HD, with 200% scaling. 22” aka 56cm is about right.
What is the problem? AFAIK a friend of mine has been using an X-based setup (IIRC with FVWM) in his 4K laptop for years and when i asked him he told me the only thing he had to do was to use ImageMagick to scale at 2x the images his theme used.
Then I brought it down with some xrandr setting... the size is right but a bunch of other things are incorrect.
I wish it were one incremental setting like it is in MacOS? Very easy to use; very easy to adjust for each monitor.
Next, if someone fixed font / display scaling in X for high DPI (24" 4k monitor) displays, it would allow more people to use Desktop linux.