Is there a way to hide that you own a game in the steam store?

I tested this now using two accounts. And sadly, as of this writing, you can't seem to hide your owned/wishlisted games from your Steam friends on the games' specific store pages. This seems like an oversight on Valve's part since you can already hide owned/wishlisted games from your profile page using the privacy settings. That completely blocks them off from appearing on your profile. However, changing privacy setting doesn't seem to affect showing your ownership/wishlist status on the game's page.

This is trying to access a friend's wishlist when their profile is set to private. As you can see, the games are hidden as they should be.

And below is what you see when you visit a page of a game that your friend owns. The friend's profile privacy is set to "friends only" and the "keep my total playtime private" option is turned off. As you can see, it shows your friend's name and the total time they played the game.

This is what you see when you visit the same page when the friend's profile privacy is set to "friends only", but with the "keep my total playtime private" option turned on. It shows the friend who owns the game, but the game time is not shown. As it should be.

Finally, this is the same page, but with the friend's profile privacy set to "private". It supposedly shouldn't display anything, but that doesn't seem to be the case.

I think it's better if you contact Steam support regarding this and tell them. This seems like an oversight on Valve's part.

Edit [15th Jan, 2021]: I contacted Steam support on this issue. Seems like the issue would be fixed if more users made Valve aware of it using Official Steam Feedback, Official Steam Help, and Steam Subreddit.

While it's a decidedly sub-optimal (and somewhat-obvious) solution, there is one work-around to this if the game you don't want to be displayed is one that you haven't purchased yet:

Set up a second Steam account and use that account to purchase the game.

Then just don't add your friends to said second account.

Reposting my (now deleted) comment as an answer.

Not much of a solution, but you can follow the following answer to "permanently" remove a game from your library. That will effectively behave as if you never had the game, and the store page won't say that you have the game in your library anymore, which gives you the impression that you would have to buy it again if you want to have it in your library again (which isn't the case; see below the quote).

Quote from the answer:

Steps

1. Log into Steam Support
2. Select Games, Software, etc.,
3. Select the game from the search function that shows up
4. Select the option: I want to permanently remove this game from my account.
5. Select the option: Ok, remove the listed games from my account permanently.
6. Repeat as many times as you have games you'd like to get rid of.

Although Steam says it's "permanent", it isn't. You can cancel the removal (e.g. if you return on the support page for that game, you are prompted whether or not you want to put the game back in your library). Which means you can use the permanent removal feature as a way to toggle the game on or off whenever you want.

The only problem to this solution in your case is, you would have to cancel the removal everytime you want to play the game that was removed. Otherwise, it is an effective way of hiding away a game you own when you are not playing it (or if you don't ever intend to play it).