Exclusive or non exclusive photography site?

To add to what's already been said, submitting same assets to multiple sites may dilute your sales potential on Adobe Stock, particularly if customers can find the same image at a cheaper price on other sites.  Something to think about.

While Adobe Stock makes no claim of exclusivity on your assets, it's possible that the other site(s) to which you've already uploaded them might have such a claim; so you'll have to check the T&C's of other sites carefully.

For Adobe stock only: yes, Adobe does not claim an exclusive access to your creations. You can sell also on other platforms, including your own platform.

You should chek the contract carefully, but it is said that Adobe do not want any exclusivity. If this is right, you can submit work already on some other stock site, and it remains yours to sell directly.