This installs the app as if it were a system app, so it can be displayed on the dock and be found in the activities menu.
That happens by writing a *.desktop file to either /usr/share/applications or ~/.local/share/applications. An example of such file that Chromium installs is
#!/usr/bin/env xdg-open [Desktop Entry] Version=1.0 Terminal=false Type=Application Name=Google Chat Exec=/snap/bin/chromium --profile-directory=Default --app-id=mdpkiolbdkhdjpekfbkbmhigcaggjagi Icon=chrome-mdpkiolbdkhdjpekfbkbmhigcaggjagi-Default StartupWMClass=crx_mdpkiolbdkhdjpekfbkbmhigcaggjagi
Desktop environments obviously do not look for those in each ~/snap/* directory but that’s where Chromium can and does write them.
As such, to make PWA work for users of the snap, I would need it to connect to personal-files so that it is able to write and read from ~/.local/share/applications.