Parkinson's disease is primarily a VATA disorder , with excess trapped Vayu being pushed into the Majja Dhatu/nervous system. (could be secondary Pitta vitiation component in certain cases)
the best Yogic postures would be Vata pacifying, to expel and eliminate the trapped Vata in the nadi's / shrotas, ( for examplePawan -Muktasana series) along with simple, basic pranayama techniques like anulom-viloma, bhramari etc.
Ayurveda offers several great herbals and other treatments for it.
The results of recent review found that practicing yoga helped improve functional mobility, balance, and lower-limb strength in people with Parkinson's disease. In addition to improved balance, flexibility, and posture, participants experienced a boost in mood and better sleep quality.