Watchdog to monitor a folder
Wait loops
I don't think that this:
    try:
        while True:
            time.sleep(SLEEP_TIME)
    except:
        self.observer.stop()
        print(&quot;Observer Stopped&quot;)

should be necessary. I would expect that if you simply join, it would do what you want - block until the observer is done.
Even if you retained the above structure, you're not using your try correctly. That except should be a finally. In other words, you don't want to stop when something goes wrong; you want to stop whether something goes wrong or not.
Pathlib
on_any_event contains a lot of os.path calls. You'll find that replacing these with pathlib.Path equivalents is better-structured. It's a more object-oriented and &quot;syntactically sugary&quot; way of manipulating paths.
Overall
I'm not convinced that writing these generic watchdog wrappers (Handler, OnMyWatch) is useful. It's subtracting from the utility of watchdog. What if you want code of your own to run once Handler.on_any_event changes some of its attributes? You could subclass Handler and override on_any_event, calling super().on_any_event to set those attributes, but that's a fairly poor data-passing pattern.
You'd be better off writing a purpose-built FileSystemEventHandler that does not have those file-component attributes, does not look at event.event_type, and handles specifically the event you care about.
In other words, this is abstraction that hurts rather than helps you, and introduces functions with side-effects that set attributes that don't make sense as attributes.