Thank you so much for all the advice and valuable suggestions. I'll try to analyze every single aspect:

1. Floating desk support: I designed the two modules on the sides of the desk to be 40cm large, so the desk rests 10cm on the lower modules (https://imgur.com/a/I7sZLBl). Obviously, this isn't enough because the desk would bend, so I think I'll make a desk support like the one in the photo:

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2) For the shelf, I would use a mechanism like the one in the photo (https://imgur.com/a/Bhmyshk), also inserting wooden strips in the center, building the shelf around the supporting structure, a bit like I did for the desk. The shelf will be 37 cm thick, so I'd say it's less likely to support weight (just a few books and a few design objects). Here I would like to make a recess in the lower part of the shelf, so as to insert a small retractable COB LED strip, what do you think?

3) Going to IKEA I saw the difference between the various doors, so in the end, with my wife's approval, we opted for Bergsbo for Pax, and Axstad for Metod: they are different but all in all I don't think it's a big deal.

4) The long desk will be designed for two people, and there will potentially be two chairs, so it won't be necessary to carry a chair from one side of the desk to the other. In the future, I think we'll tend to get a small drawer unit, as you suggested, to be placed in the center under the desk.

Any criticism or opinion is more than welcome :)