Something I really miss is an ability to clip items from a third-party computer via a browser directly into the syncstore of my database.
This is a technical impossibility as the sync store is not a copy of your database. That also means the internal structure of a DEVONthink database is not in your sync data. And guaranteed your group hierarchies from the database are also not present.
So no, you’re not going to “add directly into the syncstore of your database”.
Follow the advice mentioned by @cgrunenberg and others here.
I’d like to add to the other suggestions that if the third-party device is an Apple one you can add tags DEVONthink does recognize.
If not one solution would be if you add the tags to the file name and have a Smart Rule in DEVONthink automatically transform them into real tags. Something like Item's File Name|tag1|tag2|tag3.filetype.