After updating to e os 1.9-s-20230310268290-stable-FP4 attempting to install any downloaded apk ends with message “There was a problem while parsing the package”
Do you attempt this directly from the browser? This should prompt for the necessary permission to install unknown Apps.
You could check whether the browser has this permission in Settings - Apps - Special app access - Install unknown Apps.
Alternatively you could try using the file manager.