I have a Lenovo M10 FHD plus and it has run both the Zwift app and the Zwift Companion app with no problems. Android 10, 64GB ROM.
Lenovo use M10 as a name for whatever is their current tablet - that is, what they call the M10 changes from year to year. Under Settings | System | About tablet you’ll find your M10’s proper model name (mine’s a TB-X606F).
All that said, all very unlikely the issue. I would be looking under Settings | Storage. Mine has an additional 512GB SD card installed, though the menus show Zwift as using the internal 64GB for storage. Maybe yours has somehow got into expecting to store on an SD card even though the card is not present.