How stable should this power supply be?
How do I determine the stability and configuration requirement of the power converter's output?

Ask the loads ;)
Relays: use 24V relays.
SBC, comms modules (interchangable WiFi, cellular, Ethernet, USB hub: most likely these all run on 3V3 and lower internally and have onboard DC-DC converters to produce these voltages from a standard 5V USB supply. It is highly likely that the only thing the 5V powers is the USB ports if the device has them. If this is the case, these can run on pretty dirty 5V, since it is regulated down to a lower voltage anyway.

Small microcontrollers

Same, if they run on 3V3 and have an onboard regulator from 5V then you don't care much about the quality of the 5V. But if it's a 5V microcontroller, and you use the ADC, and the ADC uses the power supply as analog voltage reference, then it needs a clean 5V.

RS422 drivers

Might need a clean supply, consider a LC filter with a ferrite bead.

LEDs

Don't care
Basically all the above can be powered from a switching converter from the 24V rail. Please do not buy the counterfeit LM2596 on aliexpress, you can find readymade ones at reasonable prices from the usual suppliers (mouser, digikey, meanwell, etc). The datasheets will give you hints for an input filter for EMI compliance if necessary, it's a good idea to implement it. If you're not familiar with designing DC-DC converters, you will save a lot of time and EMI headaches by buying ready-made ones.

Small sensors

If it's analog, either you need low-ish noise on the power supply, or you need an accurate voltage reference somewhere, so these may benefit from a separate linear regulator. TBD on case by case basis depending on what the load needs. You can always get clean 3V3 with a LDO from your 5V, and clean up the HF noise with ferrite beads and caps.

Should it be a DC-DC converter or (multiple) linear regulators?

If you use say 15W (5V 3A) then a 85% efficient switching converter will draw 15W/0.85=17.6W from the input, so it will waste the difference, 2.6W, as heat.
If you use linear regulators, they will waste (24V-5V)*3A = 57W as heat, so that's about a kilo of aluminium if you don't have a fan, or a PC CPU heatsink if you have one, to give you an idea of the size and bulk.
Besides the electricity bill, the cost of the heat sink (and fan), plus the weight, the shipping and handling, etc, the fasteners so the heat sink doesn't fall off when the postman throws the box around, the stronger enclosure to bear the weight, with vents, air filters, dust ingress prevention, blah blah, sum total... will be a lot more expensive than a DC-DC converter.
In many manufactured products, the DC-DC converter's efficiency is not just meant to save money on the customer's electricity bill, rather it results in a smaller, lighter, cheaper, and easier to ship (and sell) product that doesn't break down when the heat sinks are full of cat hair and other junk and it overheats.
Now you worry about power stability, in your case it's simple.
If you are putting together a bunch of readymade boards that are all designed to work with the cheapest 5V &quot;phone charger&quot; the customer will use, then these don't care much about power stability. If the first thing is a regulator to turn 5V into 3V3 it will probably work down to 4V.

Is it the data rate of the comms lines, the controllers' clock, the size of the board

No, if the boards work the designers have taken that into account. Clocks and data rate on comms line are an issue for noise emissions, however.

and the distance between the sub-systems and the DC stage?

Yes, you should definitely consider voltage drop in wires, especially in the ground wire.
If you put these systems on a board you design, then you should also consider voltage drop in traces, and also use a ground plane.
You should sort your loads into at least two groups: those that draw fluctuating current (thus pumping noise into the supply) but don't care much about voltage stability, and those that need a stable voltage and thus don't have huge variations in supply current. These two groups can get a regulator each.
Note a linear voltage regulator is not necessarily cleaner than a switcher once you take the loads into account. If you connect a single board computer to it, that draws random pulses of high current depending if the CPU is loaded or sleeping, plus some HF ripple current from the switcher powering the CPU, then the linear regulator output can have just as much noise on it than the output of a good switcher. It all depends on the implementation of course, if you buy a counterfeit LM2596 from aliexpress, YMMV.
One reason to use multiple regulators is the reference for your regulator is its 'GND' pin. So if you have a board and high current stuff in a corner, and sensitive analog stuff in the other corner, and you put the regulator somewhere where lots of noise current flows in your ground plane, then the output of the regulator will be referenced to a noisy ground and will faithfully mirror that noise in its output. This applies even more if you use wiring to connect your systems.