My phone- but really because it's the key to my car! lol Also I used my alexa lists for all my shopping (grocery list, costco list, etc) and would be pretty lost in stores without the app.
Both my purse and my phone, I won't have any way to pay and my phone because of the list too and probably because I'm a little addicted to it and will feel lost.
Although - I honestly left home w/o my credit card yesterday when my DD and I went shopping. UGH She had to pay for the shorts I bought and I had to pay her back.
My phone. I'd spend the whole day worried that someone needed to contact me in an emergency and couldn't. I'd also lose access to all my reminders and alarms and have to [gasp!] rely on my brain. I don't have a computer or other internet access at work (preschool teacher), so some days that would be a big problem if I'd forgotten my phone.
Since I work remotely, I don't even leave the house every day!
I always have my wallet (which is usually in my purse but not always), my phone, my keys, and my glasses when I leave the house. I can manage without the rest.