Solution
To execute Python functions in parallel, each Python Node call must use its own unique Python session. If you make multiple parallel Python Node calls using the same Python session, the Python Nodes will still execute in sequence rather than in parallel.
The following is an example of calling two Python functions in parallel using two separate Python sessions. The single-iteration While Loops are required for the two Python processes to run in parallel in LabVIEW 2022 Q3 and previous versions, but they are not necessary in LabVIEW 2023 Q1 and later.