Having same issue in my S10e. Workaround as below.
Activate "Always On Display" on from settings.
Now unlock your phone. The green effect will vanish for the current logged in session.
Always unclock once you have received watch either automatically or by double tap (Based on the selection of "Always On Display").
Since this is going to consume more battery. Activate battery saver with "Always On Display" to reduce the battery consumption.
This issue seems to be an OS issue.
Tried booting up the phone in Safe Mode but still the Green tint effect exist. Confirming that this is not any third party app caused issue.