Also, how does one beat the king slime with no equipment? I'm not getting slime staff either.

Idk about the first problem, but when it comes to beating king slime, you can use a zombie arm

I am sorry for the criminally late reply. I'm sure you've long since moved on. I have to pro-actively subscribe to be notified of discussions and I hadn't done it until now.

I can't speak to any issues with Recipe Browser for pinky. I haven't changed pinky or pink gel from the vanilla game. I have been considering increasing the pinky spawn rate the next time I update, as it is a big roadblock to progression until you can start farming slime rains for more pinkies.

As for the equipment issue: there are plenty of weapon options through mob drops to kill King Slime quite quickly even on the hardest difficulties. The issue comes down to survivability.
You lack health, mobility and the jerk has a knack for teleporting on top of the player. The teleporting is tied to distance and King Slime's line of sight so it can be avoided so long as you survive the first teleport. There are rope and wall strats that can work, but they're finicky. I fully understand that this first fight can be a tall order, which is why I added the easy furniture config option to the mod. Using the Nurse and equipment from other NPC's is plenty to get the job done. The other option is to generate a world with either "dontdigup" or "getfixedboi" to get pre-hardmode mimics in the game which drop the usual mobility accessories.