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There is no reason to anyway. You buy from Valve, not from anyone else.
Everyone can view your Steam profile -- you've not set it to private. Whether publishers have a quick way to get a list of all the public profiles that own a game of theirs -- I don't know. There's really no use for such a list; they are interested in overall numbers, not individuals.
As for progress... they don't have access to your saves, but like I said before, they can see your achievements since they are public, which can give them an indication of your progress in many games (particularly those with achievements like "finished chapter 1", "finished chapter 2" etc.). But, again, they are only interested in overall numbers, not "your" progress specifically. Those summaries are likely to include private profiles as well.
Whether or not a Steam game can report additional information that publishers can use -- I don't know. What it CAN do, of course, is to send information to their own servers.
https://store.steampowered.com/privacy_agreement/
It's about as good as you're going to get for data not being shared to provide 3rd party's with the info to identify and advertise to you directly. Any games promoted to you on Steam are promoted by Steam themselves based on your data, not a publisher.
Post in their game hub, they know you own the game or not.
If the game has a workshop and you want to make an item of your own, they know you own the game.
Achievements were already mentioned.
They can view what amounts to the Steam Hardware Survey but broken down to users who own their game. Those stats are only from who participated in the survey, anonymously.