When you Disable the Toolbelt in the Global settings all of Tetra's Tools become slower.

Hard to Confirm, though I do remember having this Issue before moving to 1.20+ so it may be the latter. I'll go poke them about this but what to I direct them towards? Is there anything specific that the option interacts with in order to turn off the slots?

I can confirm this, but I'm a bit stumped as to why the tool belt setting influences this.

Did this issue only start with the newest Inventorio update, or was it present before? In the second case I think this should be reported to the tetra devs instead.

Is there anything specific that the option interacts with in order to turn off the slots?

That's the thing. The only thing that option does is just not creating the tool belt slots. It doesn't have to do anything weird for that, it just doesn't call the code for adding the slots.