Spotlight search useless for basic core apps

Why is the Spotlight search index not finding what seems to me to be the most obvious result for a core app?

I search for the Calendar and it gives me a bunch of useless results. I did a fresh OS update, cleaned the index, forced a re-index, actually saw Spotlight doing a re-index process - nothing helps.

Calendar isn't the only app I'm having issues with. I don't know if it's some bias, but I feel like over the years the search has become less and less accurate.

Is there a way to customize Spotlight search to first aim for certain type of results, f.e. "always search for apps first, then go to internet suggestions, etc..." ?

I mostly use Spotlight to open apps, so I'd like to point it mostly in that search direction.

UPDATE: screenshot of my Spotlight preferences at the bottom.

UPDATE 2: I changed the Spotlight preferences as shown in the screenshots below and reindexed the whole Macintosh HD. Also tried de-selecting and selecting back the Applications preference and forcing a re-index. The issues persist.

Seems like the issue is only with certain apps. Most of the apps are being the first search result suggestion, but some apps don't appear at all. So far namely: Calendar, System Preferences, Activity Monitor, Notes.

IIRC, at OS Catalina I had no issues. When I upgraded to Monterey yesterday, things started getting icky with Utility apps like System Preferences and Activity Monitor.

UPDATE 3: Ok, getting some more info from this answer and considering that I just updated from Catalina to Monterey (skipped BigSur), there is a pattern in that only built-in apps are not showing up in Spotlight. I tried adding the /System/Applications folder to the Privacy tab of Spotlight settings, and then removing it, triggered a re-index, but that didn't fix things.

Here's another example with "System Preferences":

Spotlight preferences:

1.

2.

Ok, I figured it out with the great help from comments! What I wrote in Update 3 and the info from this article: Fixing no Spotlight results on macOS Big Sur led me to the solution:

the built-in apps have been moved to /System/Applications starting BigSur (I updated from Catalina to Monterey a day ago). I ran sudo mdutil -sa to find out:

 /:
Indexing disabled.

So, I ran: sudo mdutil -i on / which would enable indexing on /System as well. Now I can also see the built-in apps in the Spotlight search results.