In your video you let go of the key right as the engine was about to catch. That first "failed" start was solely because you didn't hold the key long enough! Give it a chance to do something before you let go.
If you had bad glow plugs, you'd be expecting white or grey smoke and the starting performance would be dreadful, assuming it even started. When it did, it would be very loud and raspy and likely missing out for a few seconds on one or more cylinders.
Generally black smoke is due to over-fuelling. If the injectors are in sad shape (or original to the car
) you could have a "squirt gun" effect going on instead of a nice spray. Until the head gets hot enough to vaporize that fuel, you'd be burning drops of fuel instead of a vapor and can certainly cause black smoke when cold or under acceleration.
The injectors can be rebuilt with new nozzles, in fact this is the preferred way to do it since the new Bosch injectors come from India and the quality is lower than whale crap on the bottom of the ocean. I made the mistake of buying new injector bodies for my SDL. 3 of them cracked where the hard lines attach and the nozzles are dreadful. You've been warned.
You might reach out to forum member Greazzer, he rebuilds injectors and has a very good reputation around here for turning out good work for not a lot of money. If your injectors are old or you suspect that's the problem, it can certainly be worth your time and dough.