Related article: Send to Case - Overview
The Send to Case Gardiant add-in is available in the web Outlook but it needs to be pinned in order for the add-in to show on each email without additional action.
In order to pin the Send to Case, log in to the web version of Outlook.
In the top right-hand corner of the screen, click on the Settings (gear) icon:
Go through Mail > Customize actions > check Send to Case under the Message surface section:
Next time you select an email, the Send to Case icon will be present to use: