[ENHANCEMENT] MMU3 spool join and filament run out enhancement

[majedation]

Printer model

MK4 with MMU3

Describe the enhancement

Requested enhancement:
When the MMU detects that the filament has run out, the printer continues printing till the extruder filament sensor detects that the filament has run out (it keeps printing with the filament between the MMU and the extruder).
After the extruder detects filament run out, the MMU loads the filament from another slot (in case of spool join), or the printer asks to load new filament (in case only one filament is loaded to the MMU), then it resumes print.
This way, the 30-40 cm filament between the MMU and the extruder is used, and also prevents the filament from getting stuck during unload, this happened with me; the end bend in the filament got stuck in the MMU during unload, and the printer stopped printing and showed an error message.

Expected functionality

MMU detects filament run out -> printer continues printing -> extruder detects filament run out -> printer stops and new filament is loaded (without unloading the previous filament since it's been completely used) -> printer resumes printing.

[Mike-FUT]

I also didn't see the point so far why the remaining filament was pulled out from the nextruder instead of just slowly pushing the new one through. Especially with the MMU modifications of the Nextruder the filament run our is detected really late when the filament already left the upper idler gear of the nextruder. Very little filament left in the Nextruder at this point in time.
So when this happens why not extrude the remaining 5 millimeter to a dump until the Nextruder gears no longer transport anything and then load the new filament from MMU to Nextruder gears and slowly push that through the nozzle?

[Ro3Deee]

why not extrude the remaining 5 millimeter to a dump

Prusa doesn't poop like bambu

[Mike-FUT]

Prusa doesn't poop like bambu

It has to, otherwise filament change when running out wouldn't be possible because you can't start printing with a freshly loaded filament without purging first (unless you want unfilled areas in your print).
And right now it does it anyway (pooping as you describe it) after the spooljoin filament change.
This change requested by @majedation would mean only an extra bit of filament on the dump.