Switching to pmOS may be bit hard but can run Docker containers on Android. (Although steps differ.) About Android, if a device got adb enabled, can use scrcpy

Switching to pmOS may be bit hard but can run Docker containers on Android. (Although steps differ.) About Android, if a device got adb enabled, can use scrcpy to display and control the device from PC. Considering this, the problem is reduced in enabling adb. If the device supports HDMI-out, can use a USB-C hub to have output and PC connection. If the device supports OTG, can use scrcpy's OTG mode (or attach a mouse via an adapter) and enable adb by doing the required steps manually. If no HDMI out, have to do them blindly. But should be possible using an automation/input tool (like xdotool) to script them. (This procedure can also be used to OEM unlock if want to install pmOS.) If the device is blessed with unlocked bootloader, can `fastboot boot` a TWRP IMG (almost every device has a TWRP port) that has adb enabled by default. From PC can then set persist enable to true and push authorization keys. If cannot run a custom recovery but the device allows 3rd-party OTA updates in stock recovery, can flash an UPDATE.ZIP that does the same. Flashing pmOS is also done via fastboot. But probably need to install a custom pmOS IMG to account for the broken screen. Like pre-enabling ssh, similar to how you will do installing Linux to a remote server.