You're not obliged to leave food for your house sitter, but it's certainly worth considering leaving a few basics for their arrival, especially if they've travelled a long way, are arriving when shops are closed, or you live far from convenience stores.
Many of the pet parents here provide a welcome meal so that both sitters and owners can get to know one another before the sit starts, but it's totally up to you whether you're comfortable with this.
So, if you're wondering - should you provide for your dog sitters, cat sitters (and everything else sitters), it's up to you. The main thing is that you avoid food waste where you can by clearly communicating with your sitter beforehand about their dietary preferences and what you're happy for them to eat.
And when it comes to your pets' food, it's totally your responsibility to provide that, and you should agree on a plan with your sitter, should they need to top up supplies while you're away.