My post dated 11 Feb 2021 stated that I succeeded in exporting to another tablet of identical make, model, etc. That has stopped working.
After updating my OS to Android 11 One UI Core 3.1, I cannot export any OsmAnd files to anywhere. After generating the export file, OsmAnd provides a lengthy pick-list of candidate destinations from which to choose. It does not, however, offer to save the export file to the simplest possible location which would be to save it to e.g. the uSD card that is in the tablet drawer, or to a user-accessible folder on the tablet, or to a USB thumb drive connected via an On-The-Go cable. After choosing e.g. my Google Drive and pressing the save button, the screen flashes very briefly and immediately reverts to the initial export menu. I cannot find the newly-generated export file anywhere. Ditto for exporting to OsmAnd itself.
Fortunately, as of 2021-July-29, I can still back up / export my track files and my favourites by inserting the uSD card into my desktop PC and manually copying the discrete track and favourites files from there onto hard drive of the PC via the classical Windows method (i.e., Ctrl+A then Ctrl+V). That is OK but does not work for OsmAnd settings because there appears not to be a discrete OsmAnd settings file that is accessible to users - or, at least, not one that I can find.
IMO it would be better if OsmAnd stored, in a discrete settings file that is accessible to users, the settings, as it does for tracks and favourites. Then folks could back up or export their settings manually, via moving the uSD card to a PC.