Is there way for UXP API to know when another window such as Camera Raw Filter or Liquify is opened?
You could listen to modalStateChanged event and ask for its title (some people would call them “junk” events) 
Anyway you should take care of different languages as I believe this refers to UI. Without localization of string, this can be fragile.
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Is there an title for when Photoshop enters its normal UI (when exiting Liquify/Camera Raw).
ie: it will trigger another state “enter” event
yes… look at state._value in screenshot… and I think you could use this to double check https://developer.adobe.com/photoshop/uxp/2022/ps_reference/media/photoshopcore/#ismodal