I've been familiar with this meaning as long as I can remember and was quite surprised to find it in the OED only.
Chiefly Cookery. The quality of having a firm texture or of being
resistant to biting or chewing.
1898 A li'l ill-fortune he wants now, same as a salad o' green stuff wants some bite to it.
E. Phillpotts, Children of Mist iv. xii.
1999 The rice should be tender and creamy, but retain some bite.
BBC Vegetarian Good Food April 36/3
2012 Homemade Thai fishcakes, on a bed of still-warm stir-fried
vegetables with bite, mild chilli-flavoured sambal condiment, and
cooling chive crème fraiche.
Journal (Newcastle) (Nexis) 29 June a27
In his answer, Mike C mentioned another sense that is also applicable to food, but different from texture:
A sharp penetrating effect
The soup has a peppery bite.
The bite of the wind on our cheeks M-W
This could conceivably lead to ambiguity when describing, for example, a spicy pasta dish without specifying either the pasta or the sauce. The penne all’arrabbiata (or penne arrabbiata) needed more bite could mean that the pasta was cooked too long (texture) or that the sauce need more chili pepper (heat).