
This is a known issue with the Power Platform "Modern" interface. When you create a custom connector globally (outside a solution) and try to "Add existing" to a solution, the process often hangs indefinitely or times out, especially if the connector has specific sharing permissions or if the definition is complex.
Here is how to solve this, ordered from the easiest fix to the most robust long-term solution.
The hanging behavior is often caused by conflicting permissions.
Since your goal is to parametrize the Host Name (using Environment Variables), you strongly benefit from creating the connector inside the solution natively rather than adding a legacy one.
If you must add that specific existing connector and Solution 1 failed:
forceUCI=1 and change it to forceUCI=0 or try to access the Classic Solution Explorer via "Switch to Classic" (if still available in your region's settings).