Drafts folder in Mail continues to grow, despite being told to save locally

See this article and follow the settings written in it Mail Mailbox Behaviors preferences on Mac - Apple Support

In your screen shot the first settings is Drafts - click the drop down arrow of it and choose as drafts rather than on my Mac .

In Junk mail box - click on drop down arrow and select as spam ( not sure what will drop down arrow options will show , but it can be spam ) .

Erase junk messages - its your choice after at after what time period you want to delete ( again click on drop down arrows and select the desired option ) .

Trash mail box - it should not be " none " select the option from drop down arrow .

Erase deleted messages - if it is kept as " none " the messages will not be deleted so you have to select other option ( same by clicking on drop down arrow )

Read the article , every setting is clearly mentioned .

This is common behaviour: every short time while drafting a "draft" is saved, sort of editions. Very often the drafts are saved even when the mail is successfully sent. When the message is sent you can select all drafts in the Drafts folder and delete those, which then deletes also in the server (because it is imap).

Choose Trash in your settings as tygb said.

This is a screen shot of mail preferences using gmail account , not sure for what are your settings for the mail .Either the mail application is corrupted or you are using some unidentified apps in the Mac use https://etrecheck.com/ to find out the details and post back the results

You have to ask the service provider about this as you have switched from POP to IMAP and the old drafts folder are piling up in new IMAP account .

You can google this link a screen shot of it .The general method is if you compose a mail and close the window it will prompt to save drafts , cancel or don't save . if you click on save it will get saved in mail side bar and you can open it later , and send .

"I'm not storing drafts on purpose after the email is sent. I'm saying that drafts are not deleted from the drafts folder automatically by the OS as they should be, even when the standard fix of keeping drafts local rather than on the server is applied."

I understand. After a while the drafts should disappear, time is different between imap and pop accounts. If they don't dissappear (don't be impatient), select them and delete them by hand.

why would you store drafts after the email is sent (it is then in the Sent folder) ???

(with imap the drafts are also in internet unless you specifically uncheck that in the mail website).

As you have switched the pop account to IMAP this will always occur see this article Get help if you have issues using a POP email account with more than one device - Apple Support