
There is no other group policy or registry key setting that can help to configure specific settings to clear data while closing the browser. The above document shows the information regarding the relevant GPO and Registry but as you said it will apply to all the settings for edge://settings/clearBrowsingDataOnClose. Clear cached images and files when Microsoft Edge closes.Clear browsing data when Microsoft Edge closes.I found that there are 2 relevant group policies. I try to refer to the official documents and made tests with the MS Edge browser.
