Using New Outlook on Windows for professional communication and productivity
Displaying the e-mail you are composing in a separate window works around the issue. See previous replies in the thread, especially Kolchak63's reply on the first page of this thread (https://answers.microsoft.com/en-us/outlook_com/forum/outlk_win-outtop_new-outsub_ofh/no-spelling-suggestions-in-the-right-click-menu/2f54d6e4-2b40-4a68-a201-5ca9a095aacf?page=1).
Report this issue, if you haven't already done that, to Microsoft via Help > Feedback.