How octopi might use clothing
Octopi are an incredible order - and it just so happens that some species actually use something that could loosely be considered clothing.
Coconut octopi have been observed carrying pairs of half-coconuts or shells around with them to wear as camouflage and defense - as seen in this video. They pull the pieces together over themselves when they are lying in wait for prey or threatened. Now this is not really clothing as it is only put on when they come to rest, but you can see how the concept could be adapted into a sort of suit of armor. One of the benefits of being in the water is that it can support the weight of such armor, making it more practical than on land.
It seems unlikely that octopi would use clothing for warmth, as insulation would be of little use since they are ectotherms, so don't generate much heat. Clothing to keep them warm or cool would need active heating or cooling systems inbuilt.
I don't know about whether they would use clothing for status symbols or "decency", as your octopi analogues clearly differ a great deal from extant octopi in social behavior given that they have a whole society. Use of clothing as a status symbol seems plausible, given there are a range of similar behaviors in nature (such as bower bird nests).
However a major use of clothing you have missed is for disguise. Octopi are masters of disguise, and the best of the best is the mimic octopus. Clothing could be used to take it's disguises to another level.
What would octopus clothing look like
I would suggest octopus clothing would likely take the form of a hard shell of some sort, which the octopus can draw it's whole body into when threatened or hiding. It might even have spines.
It would also probably be modeled after something else - either a perfectly innocuous rock, or another species - so as to fool predator and prey alike.
One of the key advantages of an octopus is it's ability to morph it's body into any shape, and I suspect they would be unwilling to give up this ability lightly. Therefore I expect there clothing might be quick release, allowing them to ditch it when they need to get through a small hole.
Below is a mock-up of a possible octopus garment
This suit has the following features:
- a hinge to allow rapid removal if the suit becomes an encumbrance
- a hook for easy release using tentacles
- a faux sea urchin (with real spines) for added protection
- eye holes
- tentacle holes
Materials used for this garment
This could be constructed primarily from a piece of hollowed out coral rock. The urchin spines could be collected from real urchins (which might also be eaten). The spines might need to be replaced quite frequently, as they are quite brittle. The hinge and hook could be made from plastic/rubber which is found in abundance in our oceans, and lasts a long time. Or perhaps from biological materials, such as kelp fibers, fish leather or fibers from shark egg cases