After trying a lot of things I finally got the deployment to work again. I'm using rocker/shiny:4.3.1 as docker base image with shiny 1.7.3. In the docker build, I manually downgrade rsconnect again, as it was working before, with
remotes::install_version("rsconnect", "0.8.29")
According to this thread
https://forum.posit.co/t/shinyapps-io-deploy-error-409-application-exists-with-name/170488/13
there was a fix by Posit some 9 days ago, that's why the downgrade works again.