Your system information

• Steam client version (build number or date): build date is "Oct 13 2021, at 19:47:24"
• Distribution (e.g. Ubuntu): Linux Mint 20.2 on both host and client devices
• Opted into Steam client beta?: No
• Have you checked for system updates?: Yes

Please describe your issue in as much detail as possible:

Expected result:
Ability to stream games from one device to another provided that host device can run the game either natively or via Proton.

Actual result:
"Stream" and "Connect" buttons are absent for some games, especially those that do not list official "SteamOS+Linux" compatibility. Only "Install" button is present and it's either grayed out, or enabled if Proton is forced on client device.
Streaming process itself works fine.
Examples of games that don't work: "Cat Quest 2", "Darksiders Genesis", "Killing Floor 2", "Little Nightmares", "Titan Quest Anniversary Edition", "Semblance", "Borderlands GOTY Enhanced", "Titan Souls".
A workaround is possible and explained below.

Steps for reproducing this issue:

1. Start Steam on host and client devices, verify that they are connected to each other, and that games that officially support Linux have the "Stream" button in their library pages.
2. Find a game that does not officially support Linux, verify that the "Force the use of a specific Steam Play compatibility tool" option is disabled on the host, and observe that "Stream" is not available on the client.
3. Start the game on the host and observe that "Connect" is not available on the client. Restarting Steam on client device has no effect at this step.
4. Exit the game, enable "Force compatibility tool" option, and start the game again.
5. Restart Steam on client device and observe that "Connect" button is now enabled. "Stream" button is enabled as well after exiting the game.