Using Classic Outlook on Windows for personal email, calendar, and contact management
Based on the screenshot, Outlook is stuck on "Synchronizing." The sending process hasn't actually failed completely; instead, the synchronization of a specific mailbox or folder is slowing down the entire Send/Receive queue, causing the program to hang for 10–20 minutes.
I suggest the following:
Press the Win + R keys and enter: %localappdata%\Microsoft\Outlook
Locate the file with the .ost extension (usually named after your email account).
Delete this .ost file or simply rename it (renaming—e.g., to .old—is safer).
Restart Outlook; it will automatically re-download your mailbox data and generate a new OST file.