The only current solution for this afaik is anbox which tends to be rather rough to set up. If you do have an Android phone, my recommendation would be to try to use the integrated backup system, or if you have games, see if they have Play Games sync. Failing that, if the device is rooted, you could configure e.g. Swift Backup to backup on schedule.
For the record, the official Android emulator does store the AVD files in your home directory.