"onsleep: continue" is specified in the manifest file, but the web app's JavaScript functions don't work in the Power OFF state.

This is a known issue.
Even if you set the “onsleep: continue” option in the manifest file, the web app’s JavaScript functions (e.g. HDMI auto input change of BRAVIA Meeting) become unavailable 5 minutes after Power OFF.
This issue is fixed on WebAppRuntime v1.5.15.4 or later.