Welcome to the community!
Though, as I think you understand, it’s possible to assign both a Category and Tag column value in the same rule, you are correct that only one rule will be applied per transaction.
Here’s a solution that takes a little sheet-renaming, but might work if your rules can be split out into those that assign tag(s), and those that assign categories:
Make a copy of your AutoCat sheet, named (for example) “AutoCat-Tags”. Make sure there’s a column heading “Tag” on this sheet, and write rules to assign tags by filling in this column, but leave the Category column blank.
In your original AutoCat sheet, write rules to assign values to the Category, and remove the “Tag” column entirely. For now, rename that original AutoCat sheet “AutoCat-Cats”.
When you run AutoCat, it looks for a sheet named “AutoCat” and runs those rules. So, if you take the “AutoCat-Tags” sheet and, for now, rename it “AutoCat”, and hit the “Run AutoCat” button the rules that assign tags will be run against your Transactions. Since the Category column on that rules sheet is blank, all the category value will be cleared out for matching rules.
Then change the “AutoCat” sheet back to “AutoCat-Tags”, and rename the “AutoCat-Cats” to “AutoCat”. Press “Run AutoCat” and the rules to assign categories will be run. Since this sheet doesn’t have a “Tag” column, the values for that column that you just set won’t be changed. (It turns out that the Sheets tool won’t accept rules without the “Category” column, so that trick doesn’t work the other way).
This is pretty involved, I know - but it might be easier than trying to craft a full set of rules that match all your criteria and assign Category and Tag in one go.
Hope this helps,
Scott