Filters and LFOs turn off instantly when the BB track is muted

This bug has been around for quite a long time but I couldn't find any mentions of it on this bug tracker, so here it is.
Edit: Actually a similar issue has came up once already in #3544, so might be a duplicate.
The problem appears when a BB track contains an instrument with anything enabled on the Env/LFO tab. When you mute such a track, the currently playing notes get finished as they should, but the filters and such things turn off instantly. This causes the raw sound to be heard during the time between muting the track and the end of the note. This can be rather annoying especially if the filter does a large amount of cutoff and the volume is turned up.
Here is a project file on which you can see the problem clearly: bb-mute.mmp.gz
When you mute the TCO itself in the BB editor, these effects stay active and I think it should be this way when muting the BB track as well.
If I remember correctly, the bug was already present in versions 1.0.x, but is confirmed to be there in every version since 1.2.0.

Start by loading the attached bb-mute.mmp.gz project and comparing BB track muting with muting the TCO in the BB editor. Trace how note completion differs between those two mute paths, then verify that filters and LFO effects remain active until playing notes finish when the BB track is muted.