SSMS 22 - Not seeing the Database name information in the Status Bar and Title bar is gone.

If my new setup (Management Studio 22.10.1) is the same as yours, then the "title bar" is missing because the "Compact menu bar" option is turned on.  You can turn it off, and get the title bar back.

Start from the top menu: Tools > Options > All Settings > Environment > Visual Experience

Among the options is: (Tick mark) "Use compact menu bar - Combines the title and menu bars to increase vertical space.  You must restart the application for this setting change to take effect."

Click on the tick mark to remove it, then terminate the Management Studio app (close it, keys Alt+F4), and when you start it again, you should have your title bar.

I thought it must be there somewhere... when I searched, there's a third-party add-on, "DevArt dbForge SQL Complete", whose features include making the Management Studio title bar more interesting.  For $149.95 Standard price, I expect it does more than that - and I haven't decided to buy yet - but I'd also expect them to notice when Management Studio doesn't HAVE a title bar any more.  And in case they drop by on this thread, they're welcome by me to update their own online documentation to say where Microsoft have PUT IT.  Unless that is a Microsoft trade secret, of course.  As far as I remember, I just poked around the Management Studio screen and found it (after looking via Bing, at DevArt's web site - and also here), so if it's secret, it isn't very.