Analyze two User lists to add the data to a third list

What you have put in the Only when is what you should use in the Make a change to thing action
I don’t think you need to put a filter. Also, I don’t think you need to use the Do when …trigger. Here’s what you should do:
When user add someone to the list (my selection), trigger a workflow that will use the expression and update Matched field. Also, trigger a backend flow that will also run the same, but for the added user. You will use the same expression again to update matched field.

Now, Bubble also have an Alpha (currently under testing on few app) that will fit perfectly for your case. This can trigger a notification for example when a new match is found.

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