Calendar Sync API/APP

Description

Hello,
We run a small beauty salon. Our clients can book appointments using our website where we use squarespace scheduling or treatwell (it's like uber for salons, great to get new customers) but this calendar doesn't sync with any external calendars. Treatwell used to sync one way with google but not anymore. When treatwell used to sync one way all our own website appointments were automatically blocked in treatwell but we had to manually add blocks in scheduling (our website) when a booking was made in treatwell. Now that not even the one way sync works we have to manually block each appointment in both calendars.
We seek a developer to design and build a calendar integration solution. The software must synchronise appointment data bidirectionally between Treatwell and Squarespace scheduling platforms, ensuring dates and availabilities remain identical across platforms, including lunch breaks and days off. Updates to either system must trigger near-instant replication to the other to maintain seamless operation and avoid duplicate bookings.
We don't really need a visual interface.
We had a solution working done by webscapring by someone but it stopped working and there is not update on that.
Squarespace has an API, treatwell does not.
How would you go about it? Any suggestions?
Sorry if I didn't make myself clear, please ask any further questions.