To be clear: Automation runs appear in the Automation Monitor only if their event, including any condition, triggers.
The TODAY function returns a date, such as 1/23/2023, not a number like 1 or 7. Potentially, the problem in your expression is simply one of data types. Regardless, if you test an expression comparing TODAY to an integer from 1-7, you’ll see that it returns false in every case:
Perhaps you intend to exclude Sundays and Saturdays, in which case you likely should use instead the WEEKDAY function. If that’s your goal, then you also wouldn’t use OR. Here’s a new draft to modify and experiment with.