Yes, I can reproduce that issue as well and it appears the same as the login dialog one. My apologies, I only searched for "login". This however made me curious whether other webview-like windows are affected, and while it's a bit harder to tell because there aren't always immediately active text boxes, I'd say that's the case.
Edit: Forgot to mention, but I think the in-game overlay is not affected by this, at least I can immediately type text when I open the notes feature.
Indeed, I tried yesterday and I could reply to chat inside the overlay without the need to hover the mouse cursor above the text area.
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Your system information
Please describe your issue in as much detail as possible:
When launching Steam, the login window will have a blinking cursor in the name field implying text can directly be entered as has been the case in the past, but currently no keyboard input appears to be registered at all until the mouse is moved over the window and a few pixels inwards. Alt-tabbing and min- and maximising doesn't change this either, if you're careful you can even grab the title bar, move the window around, and still not be able to input your credentials until you move the mouse fully into the window.
Steps for reproducing this issue: