No, that is not possible to do with extensions.
As you already mentioned above, the quickest & easiest & best solution is to use Fillout’s advanced forms for Airtable, which provides dozens of advanced Airtable features that aren’t natively available in Airtable’s forms.
Alternatively, to keep it all within Airtable, you can just create another Airtable form to create new records in the linked table. You can put a link to that 2nd form on the 1st form.
Or create a dummy linked record called “*CREATE NEW RECORD*”, and then have conditional fields show up when the user chooses that. Then, you can have an automation move the data into the appropriate table.