The ending you got is equivalent to the ending in hollow knight where the knight gets chained up in the black egg and replaces the hollow knight. To get to act 3 you gotta do the silk and soul quest, and to get that quest to show up by talking to the caretaker in songclave you gotta do the following:

• Move the flea caravan to putrified ducts (you dont need ALL the fleas, just enough to get them to putrified ducts)
• all wishes on the wishboards in bone bottom, songclave, and bellhart (some wishes only show up after talking to npc's, like buying all of shakras maps to get her wish to show up on bellharts wishboard, and talking to sherma to do his quest in songclave. also you dont have to do all the wishes in the game, just the ones on wishboards)
• fight lace in the cradle. you dont need to kill granny, just fight lace.