I would set up two separate branches (one on each of your workspace), push from them, and then merge those branches to the "dev" or "prod" branch in the external tool (by creating a pull request). My favorite is Azure DevOps, but the most popular are GitHub and Gitlab.
Of course, you can have as many branches as you want in a separate folder in each workspace. So you can have on your workspace branch dedicated to that workspace as well "dev" and "prod", which are created after merging pull requests and are the same in both workspaces (so you don't develop on "dev" and "prod" branches, you make only pull to get them).