After a few attempts I've transferred my QGIS project successfully to Qfield. I'm using Google Satellite Hybrid as my basemap and need to use it at as high a resolution as possible offline.
I've tried saving the image as a raster layer (Geotiff) in QGIS using the map view as the extent (Export – Save As – Rendered Image – Geotiff – Create VRT: off – EPSG:3857 – Extent: Map View)
To which I get an error: Unsupported Data Source: not a supported raster data source. Tried various other combinations (changing data output, VRT option) but keep getting the same error.
I've also tried to create a basemap via QField Sync. I don't get an error message but when I open the project in Qfield the basemap is in the layer list but is not displaying.
I've also tried a georeferenced image saved from Google but the resolution was too low to be usable.
Best Answer
Another option is to use the Tiles XYZ plugin. You can export MBTiles at varied zoom level of your map canvas (view extent and visible layers), add the MBTiles to the QGIS project, and export them to QField.