  In this paper, we use lax monoidal TQFTs as an effective computational method
for motivic classes of representation varieties. In particular, we perform the
calculation for parabolic $\mathrm{SL}_2(\mathbb{C})$-representation varieties
over a closed orientable surface of arbitrary genus and any number of marked
points with holonomies of Jordan type. This technique is based on a building
method of lax monoidal TQFTs of physical inspiration that generalizes the
construction of Gonz\'alez-Prieto, Logares and Mu\~noz.
