Here are the results of my investigation.
If you use PsychoPy 2023.2.3 then you can embed surveys created prior to the latest update (approx 27 March 2024) but later surveys fail to return to the experiment
https://run.pavlovia.org/test-suite/surveydebugging
If you use PsychoPy 2024.1.0 (which contains improvements to the survey component) then new surveys do return to the experiment
https://run.pavlovia.org/vespr/surveydebugging
I would therefore recommend upgrading to 2024.1.0 now if you are using embedded surveys. However, I will also raise the issue with the team in case there is a simple tweak that can be made to the new surveys to make them backwards compatible.