that is certainly a better program than what was constructed (or under construction) historically. especially the scaled down size carriers would seem a more appropriate and feasible project.
I would propose an alternative, the KM had plans for ships for several purposes all approx. 6,000t. (Spahkreuzer
https://german-navy.de/kriegsmarine/ships/destroyer/spahkreuzer/index.html Minenleger
https://german-navy.de/kriegsmarine/ships/minelayer/minelayer/index.html and even a CVL
https://german-navy.de/kriegsmarine/zplan/carrier/cvl/index.html)
I do not have a projected number other than
numerous and this could eclipse the historical 40-odd DDs also in favor of properTBs* and the Spahkreuzers, the minelayers were planned for double duty from the outset anyways (so they could be used as fleet tenders and ferries also)
there is also the Dithmarschen-class which could be built in large numbers as they have commercial value during the interwar period. they could have bartered transport for oil, stockpiled more for wartime.
*TBs built off the Bremse, then an earlier TB 1939 or Elbing class, followed by actually building their mooted 1944 design (took into consideration Atlantic operations) these are all 1,700t boats, in parallel my build would have 1,700t enlarged M-boats (addition to the historical vessels not replacements)
A carrier with 12-15 aircraft could be a good fighter or recce unit, but as your source says this 6000 tonner wouldn't have been able to maintain the same speed as other KM units. The British thought that a fighter carrier that could do 31+ knots with 12 fighters would need to be 10,550 tons deep displacement.
It's hard to see what such a small carrier would do as an offensive weapon. One good internet contributor says that the early war RN scored torpedo hits with every 20th or 40th torpedo. I'd have thought it was a bit higher (I think it was 3 of 24 in the Bismarck chase). Assuming that the 3 in 24 rate is achieved by the KM, and that over half the aircraft carried in the 6000 tonner are torpedo aircraft that are used as such (that's about all that could be ranged on the short deck in two waves, and will also allow for a few fighters and recce aircraft) a typical full strike would score one hit. In the North Atlantic it seems that it was hard to run two strikes in a day (and that was on a full size carrier, with much more space and an easier motion as well as more take-off and ranging space) so it's very arguable that on average, such a ship would score two torpedo hits per day at most. That doesn't seem like a particularly efficient method of sinking vessels.
The RN figures quoted above were prepared by the First Sea Lord for the Australian and UK governments and they seem to be the best available calculation of the entire cost of running ships of different classes (which is very different from purchase price). Assuming that this vessel has a similar price/aircraft ratio as the planned 1930s UK light carrier, it comes out at 72.7% of the cost of a 35,000 ton battleship to buy and run. On a price/ton ratio the 6000 tonner is about 35% the cost of a 35,000 ton battleship, but that's way too little because workshops etc don't reduce in line with tonnage. On British figures, running 15 aircraft alone would cost 24% as much as the whole cost of running a 35,000 ton battleship. Running of the ship will probably another 18-20%. So on that basis the 6000 tonner would cost 43% as much as a battleship. Averaging out the two estimates we see a relative cost of about 57% of a Scharnhorst.
So if we axe the Twins, we get about four 6000 ton carriers with 60 a/c. One of them would have to remain on training duty so we have three for sea.
The Spahrkreuzers are about the same size as an Arethusa or Dido, so they would cost roughly 32% as much to build and run as a Scharnhorst. Assuming T and B cost as much as a Scharnhorst per ton, if they were dumped then it would be the equivalent of 2.34 Scharnhorsts which would buy you 7.3 Spahrkreuzers.
So by dumping the big ships, we now have a force of 7 light cruisers and (at best) four very light carriers. They will be up against a British cruiser force of about 80 ships, most of them equal to a Spahkreuzer in a battle. A force of 6000 ton carriers and Spahkreuzers could not run from a British cruiser, and the chance of the aircraft knocking out the sort of cruiser force the British could put up against them seems to be very slim. It's hard to see how such a force would be as much of a worry for the British as the four battleships were.
As an example, the Hipper and Lutzow and their accompanying heavy destroyers were quite powerful foes, but they did very little at Barents Sea. A Spahkreuzer would surely find it hard to get within torpedo range of a convoy with an R Class or County class as an escort, without great risk.
To get anything like 40 6000 tonners and run them, it seems that you would have to cancel all the Scharnhorsts and Bismarcks, plus all of the Hippers, plus ALL of the U-Boats, PLUS two destroyer flotillas, plus a bomber wing and a panzer division or two. (I had the calcs but lost them in tab error, but these figures aren't too far out).
On top of that it seems that you want to increase the cost of the destroyers and take the M Class from 600 tons to 1700 tons. Assuming that the 1700 ton Ms cost the same as a 1370 ton River class frigate (240k) then you'll run about 20 Ms for the cost of a Scharnhorst. Such Ms would cost about 4 times as much as the OTL Ms, assuming that the latter cost as much as a cheaper, slower and less well armed Admiralty type trawler (57k). So to 20 new Ms and pay for their running, you'll have to get Goering to throw away another 40 twin engined bombers.
I do think that a "fighter carrier" with recce aircraft could have made German heavy ships very much harder to handle (although I may be wrong because they are likely to be unable to do much to save Bismarck or Scharnhorst due to the weather those actions took place in. However, a slow ship seems to be the wrong sort of light carrier, and a KM composed of 6000 tonners is unlikely to really harm or scare the British. Finally, to pay for 40+ 6000 tonners would mean significant hits in the german army and air force budget.
(PS - while I'm not a battleship fan per se and prefer small vessels, the RN in WW2 spent about 40 million on building new battleships (the KGVs, which sank two enemy battleships) and 51 million on Coastal Forces which claimed 26 destroyers, corvettes, minesweepers etc plus two subs. Using UK build costs, the KGVs cost 40 mill and sank about 18 million dollars worth of enemy warships, giving a cost/benefit ratio of .45. Assuming that the "median" warship sunk by coastal forces was as much as a River class (which is probably a gross over-estimate) they sank very roughly 6.25 million pounds worth of ships, giving a cost/benefit ratio of .12. Coastal Forces also sank merchant vessels and E Boats, but it's an interesting illustration on the supposed claims that battlewagons were vastly expensive and of little use.
As offensive weapons, the battlewagons were clearly more cost effective which puts an interesting light on the claims that they were too expensive)
