Well, we do have one canon example of a specialized ship for ortillery: The strike cruiser in Sup9.
I cannot find the Sup9 right now, but most naval ships may be used as ortillery support, so I don't believe to make a spcialized ship for that would be too efficient.
IIRC the 4518 Lift Infantry Regiment has some SDBs as integral ortillery support.
By the way, since you also mention them: What do you see minesweepers being or doing? It has never even occurred to me that there would be such vessels because I thought that even if there are space mines of some kind, regular escort ships would fight them.
In fact it wasn't me who mentioned them. I just quoted Far-trader, who quoted Ranke when he mentioned minesweepers among other support ships. I don't remember right now to have read many things about mines in Traveller, but I guessthey could be used as point defense for some places (gas giants come to my mind)
Regarding hospital ships, you'd also want to have them because of wartime humanitarian concerns. Few of the Imperiums prospective enemies are so bitter or so callous that they'd ignore a suggestion to mutually agree not to target hospital ships. They'd be separate from other auxiliaries, and they'd be unarmed for the same reason.
AFAIK there's nothing in canon to say if there exists some Geneva Convention equivalent among the main powers in OTU, but I guess it is, and I agree with you here.
Think "Primary Combattant"="Ship of the line"≅Spinal Mount + armor
in some uses of auxiliary, anything not a Primary Combattant is an auxiliary. Littoral Combat ships and Littoral Zone Patrol Craft are auxiliaries without the A_ coding in modern US/UK use, but are military flagged and crewed
The A_ coding also implies strongly "no armor". An AD, like an AC, probably should be unarmored and lacking spinal mounts. A DE lacks spinal mounts, and by some reckoning is a support vessel - in the battle line, it dies quick. It's part of the screen, not the line.
I'm thinking "Combat Vessel"="cruisers, carriers, battleships, and some escorts", because that's what the text I've already cited twice tells me. That text then goes on to exclude auxiliaries, support ships, and scouts, so I also think that (in the Third Imperium) "auxiliary" and "supply ship" fall into two different categories.
Carriers are considered combat vessels. Two out of the three carriers we see in FS lack spinals. 'Combat vessels' include some escorts (emphasis mine). So some combat vessels do not have spinals (and presumably aren't expected to stand in the battle line).
But that's still a tangent. I'm not puzzled by what is and what isn't a combat vessel. I'm puzzled by what is the difference between an auxiliary and a support ship.
Combat vessels = Badass/big fighting ships.
Support ships = tankers, colliers, supply/replenishment, "mobile yards", non-combat-capable tenders, research craft, and the like.
Auxiliaries = Not so badass/small fighting ships (i.e. most escorts), perhaps?
Hans
I concede your knowledge about naval terminology is superior to mine, but I always thought more in ship's mission than size, and so I considered as support ships those whose main mission on the design board is not combat, opposed to combat ships of any size.
So, as I see it, a fighter or a Gazelle are combat ships, more so than a Battle Tender or a Carrier, whose main mission is not combat, but transport, mobile bases/yards and replenishment of their combat elements.
That does not mind they are main battle combatents, but we must remember most of missions (even combat missions) the Navy conducts are not main battle affairs