And do you have any stealth and jump capable carrier to make "lone wolf sneaking mission style" without the support of the main battle fleet?
No. I expect that the two scouts will operate on their own most of the time, using the carriers as transports if necessary. Being jump capable themselves, they can provide advance surveillance for any operation.
Since my empire is rather vast, with jump gates connecting all populated systems, I wanted a fast ship that can deliver a pair of slower, stealthier scouts to the outskirts. The escort carrier itself will remain in protected space. Before entering any unprotected system, the scouts will take a look before the carrier comes through. If things go awry, the carrier's speed will give them an advantage.
I would not make this ship smaller than the one you originally had, I might actually make it bigger. With that cloak it will be very hard to spot anyway. I would also consider much cheaper engines, perhaps even commercial (or close to) engines and/or use less engines. Everything to reduce the cost, this ship does not have to be fast and really don't want to move fast in enemy space anyway. I would be satisfied with a speed of 5-8000 km/s, any more than that is just overkill.
The sole purpose of the escort carrier is to transport a pair of the new scouts to a far away assignment quickly while itself remaining in friendly territory. The SEM and STH class scouts are the quiet, cloaked, jump capable ships with the scouting and surveying equipment.
I would also include a 1-2000 spaces of hangars so I can bring a few 500ton scout vessels with active/passive scanning equipment, these can be much faster. No reason to ever expose or endanger your scout ship. One additional benefit is that you now also can use it as a survey cruiser by station 500ton geological survey shuttles. Add a graviton sensor on the ship and it also become your primary survey cruiser AND scout/recon cruiser.
The escort carrier has hangar deck space for 6500 tons, enough for a pair of the 3200 ton scouts. I also considered active sensors on the escort carrier but thought that the strong passive sensors on the scouts would be enough to evade most enemy fleets. The carriers will typically remain in protected space and active sensors on the scouts defeat the purpose of their main mission; finding bad guys without them finding us. Maybe my technology will reach a point where I can design a functional active sensor with minimal EM emissions and extremely sensitive EM detection.
Enough space was available on the SEM class for the latest gravitational and geological sensors, but couldn't fit the strong passive sensors on fighter sized ships. As my technology increases, this may become a viable option.
In general it is also more efficient to build your ships bigger, especially at those tech levels. Because they become cheaper, faster to upgrade. Small ships are more expensive resource wise in the long run when you consider upgrades and retooling of naval yards and stuff like that. This is especially true with ships that you build in limited number.
Efficiency is not a big concern. I have absurd amounts of cash, resources, shipyards, and industrial capacity.
It would also be helpful to know what speed and tech level your enemy ships use and what their other capabilities are. That would most likely influence the type of scout ships you would build.
My only enemies at this time are the precursors who seem to be around the same speed as these new scouts. Unless they happen upon a very quiet enemy fleet, the scouts on their own (9375 km/s) should have no difficulty evading and escaping. As for their other capabilities, nobody I've met so far can even hope to challenge us. The scout's engines put out little heat and have a detectable cross section of a 150 ton ship.
My current battle fleets move at around 15,000 km/s, soon to be north of 17,000 km/s.
