Some references I found:
The jingle that plays when you solve puzzle is similar to the one from Zelda games.
Rare Candy is an item in Pokemon games that increases Pokemon level by 1. Candy refers to Talent Orb as "rare candy" after her first quest and these two items play sort of similar role.
Peckos - for me they are a bit similar to enemies from Illusion of Gaia:
youtu.be/wTpveWb82QA?t=81
Possibly a coincidence though.
Bouncing Ray Research Facility - first time when I went through it, I felt like it's one big reference to Aperture Science from Portal games. Melyn Ros is sort of similar to Cave Johnson, too (the way he speaks and all
I actually read texts in the facility with Cave's voice in my head, lol).
Spinsect description in the menu - 'A true believer in "spin to win"'. It's a self-reference. Spin2win is a name of Arcade mode strategy/build that was
posted on the forum and focuses on Whirlslash skill.
When hero plays the flute, Bag says: "I though all heroes can play on these things" - possible reference to Link from Zelda games, who played on ocarina.
Photon Redirection Relay a.k.a "
barrels" - reference to Donkey Kong games, where barrels had similar mechanics: jumping into one and pressing button to shoot off.
"All aboard the Shift Lift" (from BRR Facility) - reference to "All aboard the Hype Train" meme, used to express major hype for something.