Be careful what you agree to just to end an awkward silence.

Silence is uncomfortable enough that people will say almost anything to end it, including yes. That is why the pause after a request gets used so often and so deliberately. It moves the discomfort onto you and makes agreement the fastest way out, and what gets committed in those three seconds can take weeks to unwind.

Learn one sentence for the gap: let me check and come back to you. Say it slowly and let the quiet sit there, because filling it is not your job. Nothing that genuinely needs an answer now is improved by you guessing.