This is coming from someone who's never done organoid culture but I have extracted a whole lot of RNA! Do you expect the hydrogel to contain any RNA of an origin other than your samples? If not, I think a reasonable approach would be to use a blade to cut the organoids from the hydrogel (removing as much of the hydrogel as possible) and then use a tissue disruptor (such as a dounce homogeniser or a rotor-stator homogeniser) to quickly disrupt and lyse the tissue in a phenol-GITC RNA extraction reagent like Trizol or Nucleozol. Then follow the protocol for the reagent to isolate and purify your RNA.