Conjoined nerves only occasionally have significance in symptom generation. They are more likely to be involved with surgical decision making.
The L4 pars defects do not seem to be imposing compression on the L4 or L5 roots according to the radiologist but that could be open to some debate.
L5-S1 does have a right sided HNP “abutting’ (maybe effacing) the root but he does not say compression. His conclusion of “Imaging shows bilateral S1 nerve root contact and bilateral L5 nerve root contact” is lacking in a “compression” comment so I cannot interpret this as root compression.
Pain generators are diagnosed by “numbing” the structure (be it root, canal, disc or facet) and gaining temporary relief. See these: