I would like to protect myself from card testing on the Wix store; hence, I would like to at least add a reCapcha to the check out page.

Hello,

You can try contacting Wix Customer Care as they know best about the Wix Stores functionality.
https://support.wix.com/en/article/contacting-wix-customer-care-for-support

If there is no built-in option, you could also try implementing your custom payment flow:
Corvid Tutorial: Processing Payments
Corvid: About reCAPTCHA