I literally set everything in the config file to the lowest chance possible, but if I'm actually doing things in the world, I get a trinket at least once every 5 minutes, and I think that's really OP. I really wish it was possible to make unlocking trinkets actually rare. And set a seperate config for unlocking trinkets of different rarities.

What does your current config file look like. Could you please send it?

Anyways, I found some time to take a look. There's many tuning levers for balancing the mod.
You should be able to configure:

• Disable trinket drop events individually (<event>UnlockEnabled)
• Change drop chances for each event individually. 1 in 2 = 50% chance to 1 in 100000 = 0.001% chance
  Notice that higher number here is lower chance because it's a 1 in n chance of occuring.
• Cooldown (unlockCooldown) between drops: Default of 2400 ticks = 5 min and can be increased to 1728000 ticks = 1 day.
• Starting Slots (startSlots) and Maximum Slots obtainable (maxSlots)
• Starting Level cost (slotCost) and the cost increase per extra slot (slotUpFactor)
• Disabling specific trinkets (nonRandom) from dropping randomly (and then add a recipe to unlock them with something like CraftTweaker, KubeJS or datapacks)
• Ban certain trinkets (blackList) completely without adding a recipe for them.

I think this is plenty options for balancing the mod. If you have new ideas for balancing levers then suggest them.
The config file is well documented as well which is why I was suprised at this issue...
But maybe this will be helpful for people in the future.
Perhaps you could rename the issue to Powah Balancing Configuration or something for that purpose?

OH, I SEE! I think I know what my problem was. I was big dumb and didn't read the config for drop chances carefully enough... I thought smaller number meant lower chance. I didn't quite understand why the minimum value was 2 and not 1, but now it all makes sense. Thanks a lot for the reply. I feel so stupid now.