Hi Carl,
In your case, you may create a custom web app to see if it works. Below are the steps:
- Open the Access 2013 or 2016 client.
- Select custom web app.
3. Set the web location as your Team site URL and click Create.
4. Select Access under Create a table from an existing data source.
5. On the next page, browser to your local Access and click OK.
6. On the import objects window, select all and OK.
7. All objects will be imported to SharePoint Online.
Here is an article for your reference.
If the steps above don’t work, we’d like to collect the following information for clarification:
1. Is there any error message when you fail to upload the files? A screenshot is preferred.
2. Does it happen to all Access Database files?
3. What Office 365 subscription do you have?
Best Regards,
Rodney