A good relationship can survive learning that your time has other responsibilities in it.

Saying you are unavailable feels risky, so people claim more room than they have and quietly resent it later. Most relationships handle the truth better than the performance. Someone who only ever meets a fictional version of your week is not really meeting you. Saying what your time already holds is information rather than rejection.

Give the real answer next time: not this week, but the one after. Offer something concrete instead of an apology, then keep it. The people worth the time will take the honest version without needing it dressed up.