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.