Took a bit of a dive into this airtable thing.
From what it looks like, having a browser based version, which has/holds the info required to make connections, such as the required API key, is a really bad idea.
It would mean, the security key to access the database would be stored on the client side too. Which would be highly undesirable with an eye on security.
From a posts I read online in their community I see you can use airtable Node.js,
community.airtable.com/t/airtable-on-simple-web-page-with-ajax/11551/2
requiring you to run a nodejs server.
A bit of examples with nodejs from their manual:
airtable.com/developers/apps/guides/read-data-from-airtable
Having glanced over their services I see they support building custom extensions to accomadate their databases.
These are applets build in JavaScript/TypeScript and React and generally run from Nodejs.
In all honesty, using this database system with Construct seems like a bit of waste of energy spent, depending on what you wish to achieve perhaps, but alas.
They have their own system of building apps for their data.
Using it in another tool, can be done, but would be high maintenance with security issues.
Not to mention the lack of examples and likely less support to achieve your goals.
Suggestion: Stick to a database system thats been tested and trialed a lot, with known examples and lots of existing knowledge in the construct community. (mysql/php, Firebase)
As a test, ask in the airbase community if someone is using Construct 2 or 3 for front end representation of their databases.