Playback of microtonal accidentals is up in the air at the moment – playback is not sufficiently well-developed for us to be able to say how this might work. But there is at least the potential for this to be done without requiring a proliferation of MIDI channels, because HALion supports VST 3 Note Expression, allowing control of what would normally be channel-wide data on a per-note basis, including pitch bend.
As for how microtonal accidentals are handled semantically within Dorico, you can specify a tuning system with any number of equal divisions of the octave. Within that, you can specify a temperament definition, which defines how many EDOs there are between each diatonic step from one C to the C above it.
You can also define your own accidentals, which define a specific number of EDOs delta either up or down from the written note, and organise them into custom key or mode signatures. When you input music, you can shift the pitch of the selected note by a small step (in 12-EDO music, this would be a semitone; in 24-EDO music, a quarter-tone; in schemes with larger numbers of EDOs, to the next accidental in that direction), and cycle through the available accidentals that way. All of the accidentals will also be shown in one of the panels in Write mode.
We haven’t defined the Sagittal system or the Ben Johnston system out of the box, but all of the accidental symbols are in Bravura, and the features we will provide should make it possible for you to do this yourself.
At the time of writing, we do not yet have the dialog needed to define your own accidental types or tuning systems, though all of the underlying support is there. Hopefully the dialog will be implemented before the initial public release: if not, it will come shortly thereafter.