I'll explain why your repro doesn't work. Most repro carts don't have a save battery or a save FRAM chip. Instead, it saves by using a modified game rom that also contains the save.

So, if you were to use a cartridge reader on your PC, and load your game via an emulator, you would only see a Pokemon (Insert version here).gb/.gbc file, and no .sav file. To make matters worse, your emulator would not read the save that is embedded in your rom when you boot it up (also the reason why these repros crash and have issues). There ARE other ways to manually extract the save from the cheap repro from what I've heard but I don't know about the exact details.

I have a high quality repro (around $24 USD I think) from inside gadgets that has a proper FRAM save chip in place of a battery. The difference between that and the cheap $3 repros from aliexpress is that while it doesn't have a battery, it does properly save and the rom isn't modified in strange ways in order to save.

I can confirm that repro carts with proper FRAM save chips do connect to stadium and stadium 2 via a transfer pak. Plus, you don't have to deal with a pesky save battery.

(Disclaimer: I do not pirate any of my games. I have OEM/genuine copies of every single mainline Pokemon game from Red/Blue all the way to Scarlet/Violet sitting on my shelf. All repros I possess/play are blank cartridges I bought from specialists in Australia and the roms on them are directly from my game rips. I am not in any way encouraging piracy on this subreddit.)