Progressive Linkage is about switching between power amps, for the different feel, tone, response, and headroom they provide. On the Road King, for instance, you get 2x6L6, 2xEL34, 4x6L6, 2xEL34+2x6L6(Aka, the classic Mark series SimulClass mixed tubes setup), and 4x6L6+2xEL34. Each of these would usually be an individual amp. 2x6L6 for a classic fender or a Recto 50w, the EL34s for a 50w Marshall, 4 6L6s for the typical Dual Recto or most other high gain modern amps, the mixed EL34/6L6 that Mesa used to do in it's Mark series but rarely is seen elsewhere, and a full headroom 6 tube setting similar to the Triple Recto.
These lead to different levels of headroom and volume, but it's as a byproduct of essentially making switchable power amps. It literally lets you put your 50w Fender Clean, your 50W Marshall Crunch, and your smooth mixed triode/pentode EL34/6L6 ~100w lead sound all in the same amp, rather than lugging a blackface, a JTM50, and a Mark III around. It does also let you taylor your headroom/volume to the venue as well though, the same way if you owned all those amps you might pick the 50w for a smaller show. It's also the much more advanced version of
Wattage Selection, which is that idea done smaller. Without the mixing and matching of power tubes, it's still pretty easy to take 4 6L6s and shut two off to go to half power, or bridge them to triode for less power still. The Mark V does one further by having the 10w mode actually switch to Single Ended Class A on two tubes, which is like it's own totally different amp topology.
Then you have Powersoak, which is basically just a built in Attenuator for the amp. Attenuators doing one job which is not "I wish I had a 50w Marshall power section" but "I wish I could push this power section like when I cranked it at that outdoor show, but not destroy everyone's ears in this small bar." It lets you. per channel, use the master volume like a tone control, choosing how hard the power tubes work, and how much power amp overdrive you get. Then the Powersoak knob acts as a final volume control after the power tubes, letting you balance the volume and bring it down again if needed.
So they all allow you to tailor your amp and power section a bit to what you need, and can help adapt to the needs of a venue. But they do it in different ways, where the first two change the actual power amp, but the powersoak just soaks up volume to bring the level down once you've found your tone.