Basically they aren't going to impress your non-technical boss who is your boss for some inexplicable reason. Postgres has been able to function as key value store(which is basically what most NoSQL "engines" basically are, write once append only key value stores) for quite a long time now.
Writing code to query your key-value store is another story.

The rest of my admittedly very snarky, but arguably highly accurate commentary on various veins of discussion on this topic will be left in a time capsule below for future generations of people who actually have a legitimate interest in computer programming to discover after the Taliban are driven out of the computer industry.

Theoretically you can replace hiring smart programmers with magical artificial intelligence that reads your mind and then uses the computer to bend the world to your iron will, but if someone else could produce such a magical artificially intelligent database why would they share it with you? Perhaps they are an omnipotent omnipresent omnibenevolent entity that loves you just a little bit more because of your good looks and high intelligence?

Is this different from wanting to do a persistent query? Basically, since you have a programmable computer that you can program to talk to the database program, you write a computer program that periodically queries the database and then takes the action when the condition is met.

SQL is an implementation of a mathematical descriptive language for relationships. The whole point is that temporal logic like "wait until this happens, then do this" can be kept somewhat separate from logic describing the data you are tracking.

You have SQL that describes what it is you want to store, and particular questions you want to ask about what it is you want to store, and then the job of the database program is to figure out how to store the data safely and efficiently and answer your questions quickly. How you write the SQL that describes the way you want to store the data depends some on what kind of questions you want to ask, and this is what an actually skilled "Database Application Programmer" can figure out for you.

Some proprietary(and probably also Postgres) databases do provide support for the kind of thing you are asking to do here in the form of what are called "Stored Procedures" . Your average corporation accumulates an utter shitload of these stored procedures that various non-technical technical question askers in different departments don't tell each other about and they are often doing the same thing in different ways at different times. Then later they crash the database and break the application itself because there is insufficient technical oversight and communication at the actual decision making levels of the corporate bureaucracy.

Long story short, do all of this stuff in persistent queries done outside of the database and tracked in a shared medium like a wiki page, or even better a physical notebook routinely reviewed as part of management actually doing some managing.
https://en.wikipedia.org/wiki/Gantt_chart

This is an indication that you are not using a Model View Controller approach to building your database client. There are some python ORMs that were doing this automatically correctly a decade ago, but there are presuambly still several corporations with hundreds of millions of dollars using Enterprise Java Beans in 2021, also maybe some people with nuclear arsenals as well so you shouldn't consider yourself too behind the times.