Thanks for these details @lauramarie43, it really helps to understand your exact needs and look for the best solutions to meet them.
I am not aware of any existing tool to do exactly that, but you could achieve your goal by connecting a custom field and post type management plugin such as ACF (optional, alternatives exist), an “engine” to synchronize data such as WP All Import and inventory data available via Squarespace Commerce APIs. Note that I’m not guaranteeing that this is possible, it’s just a hint to explore. In any case, it could be quite a long and difficult process, even with community support, if you’re not familiar with this and maybe you’d better ask someone familiar with APIs and WordPress to do it.
Another option might be to look at litCommerce which claims to be able to synchronize Squarespace stores with Woo(Commerce) which is the leading e-commerce plugin for WordPress. This isn’t exactly designed for your needs since you don’t want to sell your products on your WordPress site, but you might be able to disable this feature, tweak a few things in Woo and the result might be acceptable. Check with litCommerce support first to be sure. Please note that I’m not affiliated with this product and don’t particularly recommend it (I’ve never used it and wasn’t even aware of its existence before). This is also just a hint that you need to investigate further.
Finally, your best option in my opinion is to ask a WordPress developer to write a custom solution for you. Your needs are specific, but they don’t seem too advanced. I don’t think I’m allowed to offer services here (you can find your way though), but there are plenty of companies and individuals offering custom WordPress development services who might be able to write a piece of code to do just that. Ask for a few quotes. There will be a cost, but the result will match your exact needs and it should be more reliable over time.
All in all, it sounds totally doable. In my opinion, the best solution to adopt depends essentially on your time/knowledge, your expectations and your budget.
Feel free to ask if you have any questions.