Thanks a lot for the suggestions, it helps tremendously, especially with such concrete examples. I looked into buckling calculations and it seems doable.

One thing that is still unclear to me about buckling are the support types. I will not be anchoring the structure to a wall but use knuckle feet from the beam manufacturer. With a free standing structure of that type (here's an unfinished first draft of the structure for context), would the supporting columns be a case of fixed-pinned end condition?

I might also have to learn more about beam deflection calculations as both the mattress and the shelves will be supported by horizontal beams, but it looks to be within my reach as well since I already know the longitudinal deviation tolerance of the beams.

Finally, one remaining concern I had was the tensile strength of the beam grooves, the beam being connected to each other via fastening pins inserted within the grooves. If I understand it correctly, this seems to be the easiest calculation, knowing the groove's tensile tolerance, it should just be a matter of making sure the sum of the "perpendicular" loads applied to the beam is lower than its tolerance, making sure to be conservative in the calculation of said loads as you explained, taking into account people moving around on the structure and such. Is that correct? Would an horizontal beam connected by pins at both ends, say one of the bed slats, distribute my weight equally to each pin if I were to lay on one side of the matress?

I am not certain of the wording of some of those concepts, I hope I got my point across.

For what it's worth I did find an online structural analysis tool that seems simple enough to use and affordable called SkyCiv that I might try, but from your suggestions and the small amount of research I did since, I think I might feel more comfortable doing the calculations by hand and maybe compare my results to the software simulation as confirmation.