Our form extension generates a unique URL for each record in Airtable. You can treat it like a webhook (if auto-submit is ON). When the URL is clicked, it will instantly update the corresponding record. It won’t open up the actual form. You can achieve this by using 2 features:
Prefill: add the values you would like to update in the form URL.
Auto-Submit: enable this option from the prefill settings.
This would allow you to include a special link in your customer's email which would let users -with just one click- update their specific record. For example, change the status to "approved". Then you can redirect them to a URL in a field on Airtable.
If the field is not being updated, then you're not prefilling the field correctly. Make sure that Airtable prefills work first, then set up the redirect after confirming the values are being added correctly.