This is where it gets tricky. I have my PM with me and just measured. Unstretched, the internal measurement for the front pocket: 22.4 cm x 16.5 cm x 1.5 cm (l x h x d) and the back pocket: 23.5 cm x 16.5 cm x 3.5 cm. Keep in mind you have to close the bag still, so the maximum depth you can actually get from the bag is about 9.5 cm at the top edge of the bag. PM, when stuffed, looks like an ugly and awkward tent, similar to how an overstuffed Coussin PM also looks like an ugly and awkward tent. PM is not a roomy bag, unless you are willing to work with it so that it's roomy.
When using my PM, the most I can do are two makeup pouches about (15.5 cm x 10 cm -slim pouches, no depth), sunglasses in a fabric slip, recto verso or cardholder (even my LV compact wallets are too bulky), keys, and a phone in the back zip. Anything more and it's either too bulky, or the strap starts to dig into my shoulder. The bulkiest items in my pouches are mini hand sanitizer, mini lotion, two epipens, and an inhaler. There are other crossbody bags from LV that can fit your essentials without forcing it. Longchamp Le Pliage backpacks in the small size would be perfect too, actually. I use my Longchamp backpack for work, and I can fit all the things you mentioned + tupperware (my lunch), and still have extra room (I usually stuff a grocery/canvas tote).
I live in NYC, and hate rummaging through my bag. It's not efficient, or safe in certain situations. For me, PM works best for a sunny day trip, or for the bare essentials for work on a nice day. Leave the umbrella and water bottle at home. Buy water at your location, instead.