Same happens on Cinnamon Desktop.
This is now fixed on my system after update 1678845529.
I can confirm, latest beta fixed it.
While it's fixed for the chat/friendlist/settings windows, other windows still are separated. Some of the windows which are still separated are game properties, single screenshot viewer, DLC manager, Storage Manager and probably a few more which I didn't encounter yet.
Could you open this issue again @tearoww
While it's fixed for the chat/friendlist/settings windows, other windows still are separated. Some of the windows which are still separated are game properties, single screenshot viewer, DLC manager, Storage Manager and probably a few more which I didn't encounter yet.
Could you open this issue again @tearoww
This appears to also be the case on my system.
Edit: Just tested opting out of the beta but at least the game properties window stays separated on both.
Still happens on my system on stable and beta 1680827821
Seems to be fixed for me now.

I can confirm, with Steam beta all windows are grouped under one icon.
This was broken again since the last comment but has been fixed since this morning (see #9551 and this beta update)
Closing as fixed in the 2023-06-14 Steam client update.
Nothing extracted yet.
Your system information
Please describe your issue in as much detail as possible:
Before a Steam client beta update this month, Steam has had all of its windows under the same "Steam (Runtime)" window in KDE's Task Manager (taskbar).
After the update windows other than the main client window are grouped under a separate "steamwebhelper" window.
The problem does not occur if I opt out of the Steam client beta, but reappears if I opt in again.
System Information
Steps for reproducing this issue: