Yes. The more bitter, the better.

Bitter denotes alkalinity (bases).

Sinus mucus is typically acidic.

This is because amino acids are the building blocks for proteins.

https://healthcare-in-europe.com/en/news/the-case-of-the-sticky-protein.html

Proteins get sticky when they are misfolded or sheared. During an infection, proteins are released as cells die.

As the proteins decay they get sticky.

Which forms a viscous "glue."

Alkaline (basic) agents can neutralize the amino acids.

That's the reason bleach feels slippery, because it destroys the proteins that allow things to be sticky.

So, increasing your alkalinity helps to neutralize the viscosity of the mucus.

So... The more bitter the tea/coffee is, the more alkaline it is.

Coffee might not be the best option though, as the caffeine is a diuretic and can make you dehydrated faster, which could hurt more than benefit.