A hydrogel is like a stronger version of jelly. More formally [1]:

"Hydrogels are three-dimensional, polymeric networks consisting of crosslinked hydrophilic components. In certain environmental conditions, hydrogels can imbibe large amounts of water or biological fluids, while remaining insoluble."

They are excellent at soaking up a suitable drug and releasing it slowly.

The only reference that I can find to hydrogels and Parkinson's is in a paper by Kondaveeti et al. [2]. Unfortunately, this is behind a paywall. But, from what I can gather, "levodopa is loaded into magnetic hydrogels". This is then released "under external magnetic field".

Even without a magnetic effect, they draw a graph showing one of their gels delivering levodopa almost constantly for over a day.

In my view, there would be considerable advantage in having a very slow delivery method for levodopa (that is, a long half-life), not because it might be more convenient, but because it might smooth out the peaks and troughs of plasma levodopa. This could reduce dyskinesia and/or allow PwP to take larger doses of levodopa without increasing the risk of dyskinesia.

Reference:

[1] "Therapeutic applications of hydrogels in oral drug delivery"
Lindsey A Sharpe,1 Adam M Daily,1 Sarena D Horava,2 and Nicholas A Peppas
Expert Opin Drug Deliv, 2014
Therapeutic applications of hydrogels in oral drug delivery

[2] "Magnetic hydrogels for levodopa release and cell stimulation triggered by external magnetic field"
Stalin Kondaveeti, Ana Teresa, Silva Semeano, Daniel R.Cornejo, Henning Ulrich, Denise Freitas Siqueira Petria
Colloids and Surfaces B: Biointerfaces
Volume 167, 1 July 2018, Pages 415-424
Magnetic hydrogels for levodopa release and cell stimulation triggered by external magnetic field - ScienceDirect

John