How to draw an LTS based on the parallel process "|" in CCS Milner's logic?
The last LTS in your question is wrong. It should be a diamond-shaped graph, where on one side you perform action $a$ then $b$, and on the other you perform action $b$ then $a$, both sides leading to $\sf Nil$.

This is because the $a$ action is run in parallel w.r.t. the $b$ action, so we get all the possible "interleavings" between such events.

The fixed LTS you posted in the comments looks right, instead.