Dear Yehuda Neuberger,
Good day!!
Apologies for the inconvenience caused and please don’t worry, let’s work together on your concern and move towards a resolution path.
As per the description shared, I would like to confirm whether you are looking for the option SharePoint while attaching the files in the email via Outlook for the web so that you no need to download from the SharePoint Online site document library and upload using “This Device”.
If my understanding is correct, I am sorry to convey that there is no out of the box feature or settings in the Outlook for the web to get the SharePoint option while attaching the files in the email.
I agree with you having the ability to have SharePoint option when attaching the files in the email via Outlook for the web will benefit the users and I request you to add your valuable idea as feedback in the Outlook · Community (microsoft.com) which is the best place to share our ideas and improve the Microsoft products.
However, the workaround you can try to attach the files in the SharePoint Online sites (connected with the Microsoft 365 groups) without downloading from the SharePoint Online site is via below steps:
Open the new email in the Outlook for the web> Click on the Attachments> OneDrive> Groups> Click on Site> Select the file> Share Link.
Note: The above steps will help to attach the file that are stored in the default document library of the SharePoint Online sites connected with the Microsoft 365 groups.
Appreciate your patience and understanding. Have a great day!!
Best Regards,
Sophia