There are 2 things you need to know about syncing mail in the Windows 10 Mail App.
Some accounts such as Yahoo, need an App Specific password, INSTEAD of your usual sign in password when setting up your account.
To create one on Yahoo for example; log in to your account through your browser as you normally would to check your mail.
Then click this link:
Click on Generate a Password, Name it something like Windows 10 Mail and highlight and copy (Cntrl+C) this password that is a series of 16 lower case letters.
Then, go to your mail app and paste this in as your new password for Yahoo. I found it easier just to delete the already established Yahoo account through the settings gear icon in the lower left of your mail app and start over.
Again, use this app password only for your Windows 10 mail app's Yahoo account. Your mail password remains the same.
2nd, and here was the big mystery for me; Windows 10 creates by default a series of folders for Yahoo that are NOT USED(!) by Yahoo. Yahoo has it's own naming convention for these folders and will create them under the "More" link, which is located below these useless folder names. If you try to sync these wrong-named folders manually by clicking on one, you will eventually receive an error message.
What you have to do is right click on all of the folders (except Inbox - which should be syncing OK), and UnPin them, making note of what they are called. In the 'More' link, you will find those folders now, and the Inbox with a Pin icon next to it, indicating that is still a visible folder in your Yahoo mail folder. Now right click and Pin the other similarly named folders you find here in 'More'. For example instead of Drafts, pin Draft (the correct folder), instead of Trash, pin Deleted Items, instead of Sent Items, pin Sent, instead of Spam, right click and pin Bulk Items.
Now! Return to your main Yahoo folder and click on these newly pinned correctly named folders one by one, and hit the Sync icon at the top of the column. (A pair of inverted circular arrows icon). Now wait until you see the folder get propagated. This may take some time.
Please report back if this works!