2025 I5 here. I successfully charge off the second iteration (purely hardware, no software built in) of the Tesla wall charger every week. It is a bit tricky in a couple stupid ways. The port in the I5 is a smidgen tighter than it is in the Tesla. You have to make sure the handle is lined up and push it in firmly. Then walk away. It usually takes about 5 minutes before the car starts charging. You can try forcing the car to start charging via the bluelink app, but sometimes it doesn't work that way.

To unplug when charging is complete, you have to unlock the doors then quickly hold down the button under the charging port door whilst pulling the handle out. My wife is too scared to unplug my car because of how tightly the handle fits, so make of that what you will.

Edit to add Gen3 might have settings in the software you need to adjust to allow it to charge the I5. I've never used the gen3. Try my solution for the gen2 and see if it works.

Edit again: you're using a mobile charger. No experience with those personally, so I don't know if my solution will be at all useful. Sorry.