I've run into this same issue.
I recently replaced a 27" Retina iMac with an M1 Mac mini. Attached to my iMac, I had an LG 27" QHD display that I used as a "magnified" HiDPI display by driving it at 1280x720 (native resolution is 2560x1440). Emails listed in my viewer window on the built-in Retina display would open onto the external display in a magnified view, with beautiful font rendering thanks to the HiDPI display resolution. Any time I wanted to see things with a "magnified" view, I'd just drag it over to the external LG display. The iMac did this running Big Sur without a hitch. When the M1 Mac mini came out, I decided to upgrade and pass along this iMac to my girlfriend.
To the M1 Mac mini that replaced it, I connected (via Thunderbolt 3) a new LG 27" 5K display that I ran at 2560x1440 (native resolution is 5120x2880). This worked just fine. What did NOT work was trying to drive my other LG display (connected via HDMI) at a HiDPI resolution of 1280x720. The mini would drive the second display at it's native resolution of 2560x1440, but not at the pixel-doubled lower resolution. This is a problem for me because I really grew to love the "magnified" lower resolution given some visual challenges (retina detachment, multiple eye surgeries, etc.).
Calling into Apple Support about this, I got the issue elevated to a second-level support person with whom I've been working for a few weeks now. Through him, I've submitted log files and screen captures from the new M1 Mac mini showing how it would not support HiDPI on the LG 27" QHD display. We also sent log files and screen shots of this same monitor connected to my old 27" Retina iMac, happily driving it at the HiDPI 1280x720 resolution. Through a number of long phone calls where we documented everything, including my particular visual needs, we put together what we felt was a very good case that this should be considered a bug that needs fixing.
Just heard back from the second-level support person with whom I've been working... (drumroll please!) Apple Engineering has said that they now consider this a bug and are committing to fixing it with a future software update. No guidance on when, but I have my fingers crossed that we'll see a fix within the next rev or two of the Big Sur OS.
Moral of the story: if you can (time and patience is required), find a path to work with Apple Support to get issues recognized as legit bugs. This can only happen if you work with them over the phone so that they can REALLY document the problem. That effort, at least in my case, has its rewards.