For years at home I used a cross-body bag for a purse. It was on the large side with a wide strap, but I didn't carry much in it, so it wasn't heavy. It's a Baggallini that I got at TJ Maxx. It worked great until it didn't. I lost quite a bit of weight and it was very uncomfortable on my newly discovered collar bones.
I switched to this small/mini, about 6 liter, Aotian backpack:
I use it every time I go anywhere. It isn't particularly secure, but I have tested it with a variety of fasteners that could be used to provide more security. I seriously considered it for my next trip, but it's too small to be the only backpack I take. It doesn't have a sternum strap, but it's so small that it's not needed. The straps loosen easily to get into and out of it and tighten easily once it's on. When shopping, I put my needed cards in a pocket of my pants or shirt. My grocery list and pen go in another pocket.
Switching to travel in Europe, I absolutely always wear a money belt to carry my very important stuff. I've tried them all, and prefer a step in style, so I don't have to worry about the things I really don't want to lose. Obviously you wear it under your clothes, not like the pictures show:
As a result, I can take a very small purse. For my originally planned Ireland trip in May of 2020, I bought a Baggallini Everyday Crossbody purse in juniper green. I have never used it, so I don't know how it will be on my shoulder. It is small (11x7x3) and lightweight (8 oz). I tend not to carry much of anything else, so I might take it on my hoped-for trip to Ireland this summer:
Many years ago, I bought two even lighter (6 oz) 9x9 Baggallini quilted cross-body bags in black and in red. I've used them many times on trips and loved them, but I don't know if they would work these days: https://www.ebay.com/itm/303650723603
I'm also considering using one of the Eddie Bauer packable backpacks I got in the past 2 years for my carry-on personal item. Both are lightweight and pretty spacious and either would have room for either of my travel purses to fit inside. Neither has a sternum strap and I haven't tried loading them up with 5-10 pounds of stuff to see how they feel.
This 20 L one is 18x10x9 and weighs 11 oz: https://www.eddiebauer.com/p/82300168/stowaway-packable-20l-daypack
This 25 L one is 17x12x6 and also weighs 11 oz: https://www.eddiebauer.com/p/82300327/stowaway-25l-pack
Note that none of these bags is RFID. I'm not much of a believer in the need for that technology.
I am a believer in straps that are sewn to the purse or backpack. In fact I've had some lobster claw clasps removed and had the straps sewn onto my purses. Lobster claw clasps that go into rings are easy targets for theft by the talented thief.