Right click on all your folders on the left hand side one by one and go Preferences -> repair mailbox and also check the last tab to see if your quota is full. you might need to make some new folders.

Repaired all folders... quotas are fine (less than 30%). Still cannot save to 'sent'.

check: have you subscribed to see the imap 'Sent' folder? Make sure it is subscribed.

• right click on imap mail account in Folder Pane and select 'Subscribe' to see list.
• make sure 'Sent' is selected and click on OK

Check Account Settings:

• right click on imap mail account in Folder Pane and select 'Settings'
• select 'Copies & Folders'
• select : 'Place a copy in'
• select: 'Other' and choose the imap sent folder on that account.
• click on 'OK'

Check size of 'Sent' folder. Enable 'Folder pane columns'. 'Menu icon' > 'Options' > 'Layout' > select 'Folder pane columns' This can also be located using 'Menu Bar' toolbar, 'View' > 'Layout' >select 'Folder pane columns'.

Select the 'Size' column. see image below as guide. What size does it give for Sent folder?

Have you ever deleted any emails held in the 'Sent' folder? If yes, have you ever compacted the Sent folder to remove those marked as deleted emails?

I just started having the same problem after I turned on 2FA on my gmail account. After I turned it off the problem was resolved.