So I noticed that your description of Global Chests says "allows the transport on all surfaces without limits" but in-game, this is not the case. The Global Chests share functionality with the Surface Chests, albeit with a separate, parallel ID system.

Personally I prefer this, but I was wondering if this is because I have Universe Chests turned on? Do the Universe Chests replace the Global Chests functionality as cross-surface, relegating Global Chests to single-surface?

How did you test this?
Check if "Force Native mode" is NOT checked.

The range of Surface Chests is limited to the current surface und first level of a Factorissimo's factory.

The range of Global Chest is the surface of the current planet and all associated¹ surfaces.
¹) This depends on the mods used. For example, for Factorissimo this is ALL levels of the factories. For the Surfaces Mod this includes all sub levels.

The Range of Universe Chest has an effect when using e.g. Space Exploration or an other mod that creates addiitional surfaces like planets/moons etc...

if you dont use any other mods. Surface Chests, Global Chest and Universe Chest doing the same.

Best regards and have fun
Kux