Data pipeline deployment using Deployment pipeline , issue with connection objects

As you've said, currently pipeline settings (and specifically connection settings are not changed between stages of a deployment pipeline - there's no rule you can use.
As far as changing the connection id, I suspect you're going to be in the same boat as us regarding this in so far as the option you might find does the trick is altering the pipeline using the API.
Couple of ways of orchestrating this - you could write your pipeline alteration code using PowerShell and run it from the many places you can execute PowerShell.
Another alternative is to use a Fabric notebook and semantic_link_labs (sempy) with the class FabricRESTClient to get the pipeline JSON, search/replace the connection string, and then rewrite it back to Fabric.
We will be using a Fabric notebook to rewrite our lakehouse/workspace ids.
I await the arrival of workspace parameters which will make some of this *so* much easier.

If this post helps, then please consider Accept it as the solution to help the other members find it more quickly.