The cartridge I changed recently was on a 100k 2010 Doblo, it wasn't noisy but was leaking a lot of oil past the bearings and smoking a lot. From what I can see of your video there does seem to be a noticeable amount of play and if as you say it is making a noise, it makes sense to change it.
Mine came off fairly easily, I oiled the 8mm spanner size bolts that hold the cartridge in place before gently undoing them, as that was my main concern, having bolts snap off
. I would say carefully mark it's exact position in relation to the body of the turbo and fit the new one in the same place, having cleaned the surface area so it sits flat and true and also so it aligns with the other pipes etc, there should be a large sealing ring that comes in your kit. Providing it sits in squarely no balancing etc. should be required as that should have been done at the factory. Be careful not to damage the vanes when fitting and make sure it can spin freely without contact on the sides or anywhere else. I also squirted oil in from both ends of the oil ways and spun it by hand to give a good startup lubrication. Prior to installation I poured oil in the return pipe to make sure it wasn't blocked and the oil drained away quickly with no blockages and then put some up the delivery pipe also. Where the old cartridge vanes were rubbing/ making a noise, check no rough marks etc in housing. As I recall the only fiddly bit was getting the bolts into the flanges of the oil ways whilst keeping the correct gaskets in place.
It's not rocket science, however I am speaking after fifty years in the motortrade, not trying to be rude, just if you feel competent, take your time and do a good job, no one is rushing you, take pictures as you go along if that helps
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It wasn't a problem on my Doblo, but some makes of car have an issue with the oil strainer in the sump blocking and effecting oil pressure to the turbo, so the turbo supplier make a warranty condition that the sump is removed and a new strainer etc. be fitted which would be a right pain if you had to do that.
Personally on older higher mileage diesel vehicles I run engine flush before change oil and filter, though apparently on newer VVT timing setups this is not a good idea.