Hello Christian,
Based on your description, my understanding is that you want to temporarily hide the original email or not include the original email when you reply to it in the Office 365 Outlook Web App (OWA), please clarify if I missed anything.
On another hand, if you like the feature in the OWA, I have found some similar feedback from the Microsoft Outlook Web App UserVoice, it is recommend to vote for the feature and leave your good ideas there. The dedicated engineers in MS would notice our
request and feedback there, they may consider to add this feature into the product and service based on customers feedback in the future, and it will make our future work more suitable. For your reference
https://outlook.uservoice.com/forums/907141--the-new-outlook-on-the-web-office-365?query=inline%20reply
Hope it is helpful for you.