I'm an avid Power Apps / Power Automate developer, and just this past week have been trying to use the connector you mentioned. It's not very good. For example, it doesn't return or accept an "offset" value to facilitate paging (when there are more than 100 rows.) The author is in Asia some place and his 'support' site hasn't had any active posts for years.
I created my own custom connector for Airtable and a Power Automate flow that handles pagination. I'd be happy to swap notes. I had to do some special handling in Power Apps, since Power Fx is strongly typed and the JSON that comes back from Airtable is not.
As far as your question goes, I've been using an API Key (yes, pretty lame from a security standpoint) and would like to move to a PAT. One thing I found while I was trying to make my connector work is that that API Key I pass to Airtable has to include the "Bearer " string. Not sure that was the case with the custom one you're using, but I have to enter "Bearer patmrNEb....bd2" as the value. Might give that a try for the heck of it.