I don't know if this is a "known issue" because I've seen nobody else discussing it in this forum. However, I too can confirm your findings.
What you are describing with StartAllBack with the widgets icon/button not opening with "classic taskbar" enabled does nothing.
Hovering over the widget though does show tooltip info on whatever is updating on the widget icon: weather, stocks, alerts...ect.
Nice to know I'm not alone here!
Windows 11 24H2 (Build 26100.712)