Ah Jordan this is such a great idea and you've executed on it so perfectly! I was able to pick up immediately which key I needed to hit, and once I got the premise my hands were glued to the keyboard trying to nail the sequence. The art you've made is ofc incredible, and really sells this little ball of something trying its best to be the pet others want it to be. And mechanically, everything feels perfectly arbitrary, where even if rolling over 3 times feels repetitive, I want to do it because I want this little slime to have a home, and the arbitrary-ness makes sense given how desperate to impress the slime is.
My only real issue is that I accidentally skipped over being both denied and adopted the first few times as I slammed the red button before having a chance to fully read it. Having the game slow down a tad there, or even just changing the colour of the button to alert me to look closer might have been nice.
But really otherwise this is incredible, from the visual design to the button choices. Great work dude!