I don’t have a Hi-DPI Display, but from what i’ve read, you can enable fractional scaling (e.g. 125%, 150%, …) by enabling the corresponding feature manually:
gsettings set org.gnome.mutter experimental-features "['x11-randr-fractional-scaling']"
Now fire up your settings and set the desired fractional scale.
(I assume that you saved the text above to a file called myfile.sh directly in your home directory). If this works, our next step is to apply this script at every boot. Play around with the xrandr scale to find something which suits your needs.
To automatically launch a application or script upon the login to your desktop session, you need to create a few files and put them into the right location.
In this tutorial, we will autoload a script located in ~/scripts/resolution.sh.
Create a launcher file
Open up a text editor and put the following in:
[Desktop Entry]
Name=SetResolution
Description=Sets the Display resolution and scale
Type=Application
Exec=/sysroot/home/egon/scripts/resolution.sh
Icon=application-x-executable-symbolic
X-GNOME-Autostart-Enabled=true
X-GNOME-Autostart-Delay=0
Adopt the Exec path to reflect your actual home directory. The last two lines aren’t really necessary, but give you some kind of freedom to enable/disable autostart and optionally set a launch delay.
Save this file as ~/.config/autostart/SetResolution.desktop
Mark the launcher as trusted
Open up a Terminal and enter:
chmod 755 ~/.config/autostart/SetResolution.desktop
gio set ~/.config/autostart/SetResolution.desktop metadata::trusted yes