SOLO and MUTE shouldn't send MIDI on/off to VST Instrument Tracks

What you show in the first video when clicking Solo on the Folder Track, is the actual issue caused by MIDI Chase.
Since the MIDI Track is already playing, toggling Solo is not expected to retrigger the notes, but it still does.
That is the only real issue and it only happens with Folder Tracks.

What you show in the second video is the expected behavior of MIDI Note Chase when you get out of the Muted state.

You can configure MIDI Chase in the Preferences. MIDI Chase reads the preceding MIDI data in order to retrigger the notes the cursor is currently on when you get out of the Muted state. This is especially useful on slow pads and strings.
When MIDI Chase is Disabled, the notes won’t be retriggered anymore, but they will stay silent until the next upcoming notes are read.

Also, I’m not sure you’re constantly hitting the Mute and Solo buttons that fast when listening to your track, are you? If you feel better with it disabled then just do it, just that you’ll hear very long silences on some tracks which isn’t great either.
The issue with pressing Solo on the Folder Track has been reported already.

This is the issue 4 in the issues list.