For any instrument, I can set up in Reverb Effect in the Mixer like this.
However, for Halion SE, it looks totally different. It seems to me that it offers only Midi effects:
What is going on here? How could I apply a Reverb effect to the Halion SE channel?
The Halion SE channel only offers 4 Post effect slots in the Mixer while other VST instrument channels offer 11 Pre effect slots only.
The “Halion SE Brass” is a MIDI Track in your case.
If you want to silly dedicated Reverb, use the multi-out option and add the Reverb to the Audio Return of the Instrument Track.
What do you mean by “Midi” track?
It’s not an audio track.
However, all my other channels are not audio tracks as well, but I can still assign a Reverb effect to it.
Why can I for example assign a Reverb effect to a track that has Omnisphere VST, but not to a track that has the Halion SE VST?
I mean MIDI Track. Add Track > MIDI, adds MIDI Track. You can route the output of the MIDI Track to an already existing Instrument Track, or to the Instrument Rack or to an external hardware synth.
Then the other tracks are Instrument Tracks.
Because this as an Instrument Track.
Because this is a MIDI Track.
Read the manual…
and learn what is the difference between audio track and MIDI track…