Your Flatpak version does not support the expose-pids flag,
which means that Chromium is unable to run. This generally
happens if your distro's bubblewrap installation is setuid
instead of using user namespaces.
Also reported by another user in the forum discussion
There the RCA and proposed solution by @Harvey is:
Can confirm bubblewrap is setuid
Other distros seem to have --with-priv-mode=none or ship two packages to cover both options.