What do you give your Sector Dukes as a warship to keep the lesser Nobles on the straight-and-narrow?
(Bit long but it helps me get MTU clear in my mind)
I guess the answer to the question depends how you set the power structure up.
There are "colonial" fleets in the OTU which I assume are the feudal-like fleets each cluster/sub-sector creates.
So IMTU the Dukes control those colonial/cluster fleets - they might be run day to day by the Admirals (colonial not Imperial) but the Duke is the CinC. The IN fleets are separate.
This would be similar to the Ottoman empire where the Sultan created a professional force called Janissaries to counter the constant rebellions from the nobles. If you just have the equivalent of the IN then the Admirals in remote regions will rebel (like Roman generals did) and if you just have feudal nobles then the Dukes in remote regions will rebel - but if you have two separate power structures then the Sultan/Emperor can use them to cancel each other out.
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So if you accept that idea of a dual structure with the feudal fleets as one pillar then the type of ships the Duke would have under command would depend on the planets in the sub-sector.
The main systems in a cluster would raise taxes and some of it would go to the center to fund the IN and some would be used to raise the Ducal forces.
It could be all sent to the Ducal capital and all the ships built there or the higher tech systems could build a squadron or two each depending on size and tech or if none of the systems were high tech enough the money could be spent ordering ships from a higher tech system to be delivered or a mixture of all three.
For example
Glisten
http://travellermap.com/?scale=90.5078125&x=-94.775&y=43.597
Glisten is TL15 so could build up to IN quality ships for the colonial fleet with Ffudn and Bendor maybe building TL12 squadrons for some reason - for example can a TL10 system crew a TL15 ship from its own population easily or would they mostly have to rely on outside contractors (which is how its done in a lot of places around the world now)? Maybe TL12 ships are a better compromise for lower tech systems.
Mora
http://travellermap.com/?scale=90.5078125&x=-86.488&y=53.132
Mora on the other hand has three alpha planets: Mora itself, Palique and Fornice and I think in a situation like that Palique and Fornice would insist on producing some of the cluster fleet themselves both to subsidize their ship yards and to keep up with technology.
(To my mind the power situation in Mora lends itself to Palique and Fornice having Counts and a lot of rivalry between them and the Duke.)
So IMTU the Counts of Palique and Fornice would buy in at least one squadron of TL15 ships as the core of their fleet - in the same way countries on earth buy a few squadrons of aircraft they can't maintain themselves - but also build other squadrons themselves in their own yards with those Count's fleets nominally (and usually) under the control of the Duke.
Aramis
http://travellermap.com/?scale=90.5078125&x=-85.837&y=71.108
Aramis doesn't look like it has the ability to build much so would buy in most of what it needed.
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So after all that if you accept the premises I'd say unless the sub-sector is very backward that most sub-sector Dukes are likely to have at least a squadron of TL15 or TL12 battleships - bought in if necessary - and a feudal levy of anything from TL9 to TL15 ships from the various A star port systems in their cluster with high enough population and TL.
However that's war-fighting ships.
I can also imagine a Duke having a custom made flagship type ship like a mega-yacht: J6, M6, lots or armor and all the best defensive systems, the best comms and sensors and at least a company of marines with whatever weapons will fit after all that.
Thirdly and in this context I think there's the possibility of a riot squad category - ships for dealing with situations below war fighting - a bit like the Ducal equivalent of a Broadsword.
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So in terms of those three categories: 1) warship, 2)Ducal flagship, and 3) riot squad I'd say the OP design is a cross between the idea of a custom built Ducal military flagship / mega-yacht and a riot squad ship.
Personally I think I'd split it into two and on the one hand have a kind of top of the range Ducal military yacht which carries troops but mostly for close protection and on the other hand riot squad ships which are like bigger, meaner Broadswords with a higher troop to heavy weapons ratio than regular military units to match their paramilitary role.
IMTU the Ducal flagship would be hanging back in orbit with the Duke sipping wine and watching through the viewport as the Uber Broadswords pound the planet and send dropships to the surface.
Although actually it could vary with the Duke's personality - some of them might like to lead from the front in which case the OP design might suit well.