I hang them on my chair back, which is why I have a strap on every bag I carry.
I won't hang my bag behind my chair because who know anyone will steal it or probably the person behind (if there's another table behind me) me accidentally will dirty my bag with food/drinks. 🙄
I always will ask for an extra chair from the restaurant to put my bag. Otherwise, I will ask for slightly more spacious sitting area. If the restaurant is really overly crowded or the sitting layout is too cramp then I won't dine in that restaurant as I don't want to risk getting my bag dirty! 😅