I think that SEP & TMG are considered a class of aeroplane. You can get an LAPL(A), someone with an SSEA could also get an LAPL(A); you will both be restricted to your class of aeroplane. If you do the SSEA conversion first, your LAPL(A) will not be limited to the one class.*
There's a picture of the new licence format on p22 of
this CAA document. I suppose that no.5 & possibly no.10 are where your class & type ratings/privileges will be listed.
Bizarrely, if you zoom in on no.13 there are abbreviation explanations for SSEA & SLMG, neither of which should appear on an licence "Issued in accordance with Part-FCL".
* provided that at the time of licence conversion, your SLMG & SSEA ratings are both current.