A amx 13 with a 105 doenst have to be an SPG.
Google this: amx-13/105 modèle 58
and what i know is that even some barrels got drilled bigger, to use the 105mm shells.
their is even one in a dutch museum were i went https://www.nmm.nl/zoeken-in-de-collectie/detail/270537/ it is in dutch but maybe you can get some details out of it, or i can translate it.
if you press: meer informatie, you get all the info on the tank
In Wot, they dont put all the models in the game, and a very large amount of the tanks in the game are not completely historycle.
,wrong engine, of a gun it never used or was to big.
i hoped this helped a bit
Janeau