@Vero For me, the offending setting was Secure Keyboard entry. When I turned this off in both from Terminal > Secure Keyboard Entry as well as iTerm 2 > Secure Keyboard Entry, Alfred's Launcher behavior was restored to normal. Hope this tidbit of information helps. Credit goes to iTerm 2 developers for pointing out that this could be the issue. I had posted this over there as well because I wasn't sure the bug was on Alfred's end or iTerms end.
With regards to the vanilla account, it is possible that this setting is turned off my default for the vanilla user account. Given that the purpose of Secure Keyboard Entry is to prevent key-logging, this mechanism is probably interfering with Alfred's ability to launch. Why this was not an issue in Catalina, I do not know; but the context seems similar (vis-a-vis, losing Alfred after clicking a password box). Probably Monterey upgraded/updated security.