No, in my opinion you are not overthinking it.
It definitely sounds like she is panicking over hitting the 'big' 30.
Next time she brings up the age thing, in whatever way, just laugh and say, "Honestly X, you need to get over the age thing. Soon you'll be be 30 and then after that I'll be 26 and that's just life sweetie (or whatever endearment you would normally use for her)." If you laugh it off by facing the thing head on she should back off. She wants reassurance that you can't give, which is sad, but taunting you is unfair.
Set yourself a tiny goal each day. Or every other day. Or even once a week.
Today I will clear those dishes.
or Today I will do just one load of laundry.
or Today I will eat a light meal and I
won't let it upset my tummy.
Been there and honestly, watching the things around you go to pot only makes your mind set worse. I found that seeing small tasks completed helped me feel "Well I'm not as useless as I thought. " .... and they build up until eventually you've caught up and got a sort of routine. It might take ages but it's a goal.
It's this fucking covid crap. Everything is messed up, especially our heads. You truly aren't alone, honestly. Good for you recognising the rut, that alone is a positive.
I'm so glad you have a dog. Cuddles and petting and walks are all good therapy. And music. Seriously, make a play list of your favourite bouncy songs, put your head phones on and just get lost in the moment. I really found music great for getting through my head fog and giving me just a tiny teeny spark of "Yes!" and a smile.
Try not to think of your friends' burdens. Focus on you. Just you.