Cursor charges the “Cursor Token Rate” for BYOK https://cursor.com/docs/models-and-pricing#cursor-token-rate
It is for 3rd party models (which you get double the amount of your sub price as usage).
Of course they wont charge you extra for BYOK. how would they???
> On Teams and Enterprise plans, third-party model requests include a Cursor Token Rate of $0.25 per million tokens. This rate applies on top of model API pricing for included usage, on-demand usage, and BYOK usage.
See the link I posted above or also this one: https://cursor.com/help/models-and-usage/token-rate