Inbox shows 100s of unread emails, but actually I can only find about 58

I notice the category is “Promotions”. I don’t know where this category came from, it certainly wasn’t me.

So it does sound like you have V10 Categories enabled being your screenshot shows “Category: Promotions”.

So click on “All Inboxes” Under Favourites at the top left and see if you have a “Promotions” Category Tab along the top of the Message Subjects as in the below Gmail acct example screenshot.

If you do then have Categories, then when you installed or upgraded to V10 “you chose to enable Categories which was the default option”, but that can be changed to suit you or can be disabled as well. See this link as i posted further up the thread on the options you can do.