After switching to an Apple Silicon CPU, I'm now hunting down all the Intel-only binaries on my system.
Using the Activity Monitor and ordering the processes by Kind is quite helpful for this.

So I identified Syncthing to be still running as an Intel-only binary with the Rosetta 2 emulation.
My installation of Syncthing is quite old, so it isn't managed by Homebrew yet.
This actually made the switch quite easy:

• Shutdown syncthing
• Download latest release zip for macos-arm64 from https://github.com/syncthing/syncthing/releases/latest
• Remove the old binaries:

  rm $HOME/bin/syncthing
  rm $HOME/bin/syncthing.old

• Unzip the downloaded release and move the syncthing binary to $HOME/bin/syncthing
• Kill all running syncthing processes (they are auto-restarted via launchd)
• You might get a popup to approve the newly downloaded binary when launchd does the restart
• Check in Activity Monitor that the running Syncthing processes are now Apple binaries 🍏