The Korean ship has 3 landing crafts. The last one is in well dock. However it is nowhere close to Juan Carlos I class (on which LDP Anadolu is based) in terms of specs. Personally I believe Royal Australian Navy should have not bought Canberra Class (another Juan Carlos I class ship) if they had intended to use them as a carrier for F-35B rather than a helicopter carrier.
Most of LHD with sufficient deck area and properties can operate F-35B (following minor modifications, adding electronics-communications needed). Considering that ships are long term acquisition (about 40 years with possible extends), leaving a skip-jump on a ship which allows for easier conventional take off is a bonus. Moreover, there were other perks of Juan Carlos I made it chosen for Canberra class*.
Removing the ski-jump physically** will not increase number of simultaneous heli operations on the deck***, it could provide additional flat area for elevators but Juan Carlos I has sufficient area for those as well. The other parts related with aviation, ie. hangars, facilities below flight deck can be optimized for mixed use or rotary aircraft only, will conclude whether its most efficient for heli or jets.
*it was larger, allowed for more space, more personnel, more assets to be carried.
** %60 of the ski-jump is provided thanks to extension of the fore profile. once its made flat, this part would be diminished (or even up to %80, since in this case it will have a blunt fore, instead of pointy one ( like mistral) ). refer to the image below.
***However it can affect landings approaching from the fore
Note that, this image assumes the profile would remain same,however it would be altered slightly that yellow line would have been shifted towards stern more than shown in here.
Red line- flight deck's base
Orange- possible extension of flat deck
Yellow- actual extension of the flat deck
Green - end of the current operational deck.
Correction: removing ski-jump and extending flight deck up to the foremost point
can enable one more landing spot at the fore if it was extended up the foremost point. In case of a flat flight deck, Juan Carlos I will also have a blunt (flat) fore like mistral, which again may not be able to provide any additional landing spot.
Mistral, which was the rival of Juan Carlos I for Canberra class has 6 landing spots as well. DCNS has offered slightly larger version, i doubt if it would add another landing spot.
RAN probably should have bought something without a ski jump since they are more suitable as a helicopter carrier. Canberra class can operate only a handful of F-35B after heavy modification which would severely hurt its capability as an amphibious vessel and cost Australia a lot of money.
If they had planned to operate F-35B or C to begin with, they should have bought something much larger and probably a proper aircraft carrier.
F-35C is never an option for Juan Carlos, it doesn't have catapult or arrest wires, yet the sufficient place for those.
We are living in a time where light AAW and multi-role frigates are gaining an interest in most of the navies, thus it is reasonable for RAN and TN to choose Juan Carlos I, it is multi-role*. One step above, you will end up having an aircraft carrier which will take you into another league. RAN could consider and afford** having an AC but this isn't the case for TN.
Finally, operating F-35Bs from an LHD does not yield to "major modifications" as you have thought or reduce its amphibious capabilities***. USS Wasp operated F-35Bs, Japan has been interested in operating F-35Bs on its LHD. There are other countries considering to operate these aircrafts on their flat-deck LHDs. It is a cheap solution compared to purchasing an AC and maintaining it.
*However it takes longer time for the ship to be "fully operational". A navy purchasing a multi-role platform is as well aware of the burden to keep it active for all the role,and the crew trained.
**None of the countries with capabilities to build an AC would sell it to Turkey, neither turkey would buy it. But once Australia declares an interest, there would be several offers.
***If you mention simultaneous amphibious and aviation activities, yes it would reduce. But this is already expected. Pure amphibious or pure aviation capabilities would remain the same.