"My inbox is filled with offers from sellers that are from me looking at their product. Not saved, not marked as favorites, just looking. As a seller, I look at similar listings".
When you are on a listing page for an item, then click on the Sponsored listings on it. That is what is generating offers being sent to you. Those sellers pay extra for a listing to be sponsored and many select a percentage discount to be sent to anyone who opens the listing. Those are actually Promoted listing campaigns a seller sets up but are displayed in Sponsored listings.
You may also see some listings on search results pages that have "Sponsored" just above the item title. Opening one generates an offer to be sent.
Which inbox is being filled? Is it your ebay messages one or your regular email inbox?
If it is your ebay message inbox. From the list on the left click on From ebay then the offer and Other messages will be shown. You can use the top check box to mark all of them then click on the trash can symbol to delete them with one click
