The CAA reference page is out of date. The use of a Medical Dec on an EASA aircraft has been extended to 7th April 2021.
Licence privileges will be restricted to the class or type of aircraft used for the skill test.
This is for initial issue not conversion, so if you have a SEP rating you will be able to fly aeroplanes but not TMGs, the latter will require a Skill Test so that the privilege can be endorsed on the licence. If you were converting to a LAPL and had both SEP and TMG or SLMG privileges that were current you would get a LAPL with both Aeroplanes and TMGs endorsed upon it.
It will be time to call the local CAA to ask about the conversion or whether they have any news on EASA including LAPL privileges on the PPL.
I wouldn't bother, AOPA might be more up to date.The UK CAA will only read the same answers that you can read on line, they no longer have anyone who knows anything about aeroplanes.
I may be wrong but I seem to recall you can operate a PPL on a LAPL medical with the LAPL restrictions and retain the option to jump back to PPL with a class 2 medical.
That privilege is not included in the Regulation, it is in a CPL but not a PPL and AOPA has been persuing this with EASA. Its probably just another case of badly drafted regulations.