Hiding "add to cart" button on limited products

Site URL: https://www.californiagarden.co.nz

I have some code running on my site which hides the add to cart button on products that are sold out, I'm wondering if I can do the same thing with products marked with the "Limited Availability" badge.

The purpose is to have security around accidentally selling products that we don't have in our physical store. Our squarespace website is linked to our POS system so items pull their stock levels from there, but we want to have room for error where products that have a stock level of 5 or less are not available to buy.

Anyone have a solution to this?

Website URL: https://www.californiagarden.co.nz

Testing page: https://www.californiagarden.co.nz/test-store

Password: CaliforniaHG

Thank you!