Operation successful, patient lives:shut up:
The rattling and drones are gone; now only a slight air noise is noticeable. So it's not completely silent; that would have required further reduction of the speed and adjustments to the radial fan, but I can live with that. I didn't want to overdo it; the thing needs a bit of cooling.
Now for the report...
First of all, credit where credit is due: Without DerKuro 's pioneering work, I would never have dared to do this.
Furthermore, I'm not an electronics engineer and would like to emphasize that this is nothing but amateur tinkering. I make no claim that my work is good, and I don't see this as an instruction manual. Anyone who does this does so at their own risk.

Some people will probably throw up their hands, but it worked for me.
Material used:
-
Nanum SE-F6010 60x60x10 60 mm case fan 4-pin PWM
-
Phobya Mini PWM Adapter
- 2x
Noctua NA-SRC7
Anhang anzeigen 758195
Tools used:
- 2x spatulas à la iFixit
- 2x old plastic cards
- Electrical tape
- Side cutters, cordless screwdriver and 3mm drill bit (only for working on the fan)
Total duration of the event: With my skills, about two hours.
Preparation a): A smoking

For the teetotalers perhaps a valerian:shut up:
Preparation b): Cut off the fan frame and drill a 3mm hole in the wide bar.
Step 1:
Reapply the protective film to the glass. Place the monitor on a secure surface. I did this on a bed and placed a pillow in the middle. Loosen the four screws behind the VESA mount.
Step 2:
Carefully open a gap in the frame with the spatulas. I started on the short sides because it was easier there. Then slide the cards into the gap and feel for a clip. Something like this:
Anhang anzeigen 758208
Gently apply pressure until the clamp pops out. Then do it in a circle. It's a bit tricky, but once you get a feel for it, it's manageable. It was still very time-consuming for me...
Step 3:
Be careful when removing the back panel; the right side contains ribbon cables for the lighting and joystick. These can be easily removed by pulling them upwards.
Anhang anzeigen 758212
Step 4:
Now the interior is revealed. The metal cage containing the electronics can be completely unscrewed, but first the ribbon cables must be removed. Again, extreme caution is required here.
Anhang anzeigen 758213
a) For the cable on the right, the holder must be folded upwards to open it:
Anhang anzeigen 758214
b) The cables above the mangy fan can be easily removed:
Anhang anzeigen 758215
c) At the bottom of the USB ports, the holder must first be opened by folding it up:
Anhang anzeigen 758216
Step 5:
Now the metal cage can be carefully lifted slightly. A small ribbon cable connected to a small circuit board (temperature sensor?) can be released by flipping open the holder. The two wide ribbon cables to the driver board (?) can be removed by pressing the tabs on the sides together.
Anhang anzeigen 758218
The power supply cable can stay attached. It's long enough that the metal cage can now be completely folded up.
Step 6:
The back of the motherboard is revealed. The silver screws need to be removed; two are located under the black plastic strip.
Anhang anzeigen 758220
Step 7:
The PCB can then be pulled back a bit and out of the holder. It can then be folded over to the other side on the left.
Anhang anzeigen 758221
Step 8:
This is pretty self-explanatory. Remove the fan and screw in the new one. Since this one can be attached with just one screw, I clamped a piece of foam between the back of the engine and the radiator to prevent vibration. Then wire it up and glue it in place.
Anhang anzeigen 758222
And now everything is back together...
Conclusion: A lot of effort. For me personally, it was worth it, as I was only faced with the choice of tinkering or continuing with LCD. A TV was never an option for me. I wouldn't recommend it.
In retrospect, it turned out that a 70mm fan would have been a good fit and it would have been better to use three low noise adapters in series instead of two.
The case was able to be resealed without any external damage, and there are no warranty seals. However, there are certainly traces inside that a resourceful Dell employee could detect even after disassembly. I'll leave uncommented whether such a thing would even be investigated and the legal aspects of such an operation.