You might be able to do the release of what is mentioned here: https://www.reddit.com/r/AnaloguePocket/comments/zrwryl/backup_save_data_from_physical_cart_on_the_pocket/j1dknni/
Create a save state (memories) when playing your actual physical game, then do as that post above instructs, however load the memories playing a rom of the game via the Spiritualized GBA openFPGA core. You would then save in game and have a raw save file that is compatible with PKHeX. That could in theory work, however I have not tested that.
This post is worth a read in regards to Pokemon on the Analogue Pocket: https://www.reddit.com/r/AnaloguePocket/comments/11fpbat/definitive_guide_to_playing_pokémon_on_the/
If you have a DS or DS Lite + Flash Card, using the homebrew app "GBA Backup Tool" is by far the easiest way to backup and restore a save to a genuine GBA cartridge.
A similar save tool could eventually be created for the Analogue Pocket, however I don't think such a tool exists yet.
Edit - this looks another potential way to extract the .sav from the .sta file you have: https://www.reddit.com/r/AnaloguePocket/comments/10ampwi/solution_for_extracting_pokemon_emerald_cartridge/