Can you get any peace of mind from the fact that you have put effort in, you know the problem isn't with you? You've done your part, and they are the ones who, if they reflect, might feel a pang of not being good company or a good friend/relative.
With regard to feeling burnout, consoder what is worth your effort and eliminate what isn't. Eg I'm still up wrapping, (been too busy to wrap before now, you see) but my kids faces in the morning will make it worthwhile.
On the other hand, half our dinner tomorrow will be freezer to oven things like roast potatoes, Yorkshire, cos none of us feel the difference is worth the extra effort of making from scratch. My house isn't as clean as I'd like it to be, but its only me that notices. Try to think about what you need to do for your own benefit instead if living up to other peoples expectations.
I think a big factor in how people respond to the question "how are you?" is the tone and eye contact given when asking it. The words used are such a tiny part of communication, tone, expression, body language can carry as much weight as the words used. Equally, if someone made good eye contact and replied 'oh you know peggy, this time of year, I'm just so busy, like everyone else I guess", its very different to a crisp "im very busy". You haven't got any extra info from the answer but its not as dismissive. I'm cross on your behalf that you went to the effort of cooking for someone and they didn't have the manners to engage with you. If you'd like to cook dinner for me, I can tell you in minute detail what's keeping me busy. 😉