In my town, which is a neighborhood in a suburban location in Massachusetts, barefoot walking is common once the summer starts. I'm old and stay cold longer than most, so I don't even switch over to sandals until long after people like you have taken off your shoes! My "winter feet" are soft and vulnerable, so it takes time to build the callous and thicker skin my "summer feet" need to protect from burning (to a degree), and being vulnerable to some of the small shards of things.
I advise looking out for bigger rocks/stones. As your feet get bigger, so do the spaces between your toes, leaving you more susceptible to something getting caught between them, or in the space (arch) under your foot. Those can make you fall, and can be true on all the different surfaces you mentioned.
In the most polite way possible, I'd also like to mention droppings from animals (scat). We have strict laws about cleaning up after your dog on the sidewalk or on people's lawns, but I don't know if you have that. Still, I have to remember to frequently look down on the sidewalks and roads as I walk. The same is true in your yard and on the trails. There can be diseases present in the scat, and sometimes hard things like berries which stick in your feet. You probably know all that, since that falls into your Mum's category of diseases.
Animals also dig in the yard, and along the trail. I've often stepped into holes I didn't know were there and twisted toes and even an ankle. I even fell once and hurt my knee. Shoes can be helpful for support at times like that. I spend many hours in my garden during the summer, and always keep something on my feet, usually sneakers.
There are a few more things that pertain to all of the areas where you walk. Tree "droppings" can be annoying, and potentially dangerous too. Nuts and acorns can be tripped over. Sap can be sticky and liable to cause a fall. Pinecones can be sharp enough to cause open sores. If people on your street have lots of trees, that may be an issue. The same is true along the trails you mentioned. Also in the yard and on the trails, certain insects, like ants, can bite if you step on them, and bees can sting. There's a type of bee called a miner (or mining) bee that builds its nest in the ground, like anthills, and they can sting if you step on them. As I got older, I would go deeper into the woods and encounter things I didn't used to before I hit your age. If you're doing that, you might be technically in more danger of hurting your feet.
You obviously know about things like rusty nails, discarded bottle caps and other sharp litter. Since you're an experienced barefoot-walker, I'll bet you've been careful of those your whole life!
In my area, younger kids leave things lying around on the sidewalks, like small toys, or even bigger things like skateboards. I've often had to step out of the way, or over these things, so as not to trip. Shoes can offer protection if you do step on something like that.
This may sound silly, but as I got older, I paid a lot less attention to what was on the ground and more to the people I was walking with, like friends. If that pertains to you, it might worry your Mum. You didn't say that though, so I don't want to put words in her mouth!
If you don't mind, I'd like to share a quick story from my life. When I became a teenager, I was allowed to go alone or with friends into stores, restaurants, and other places where bare feet weren't allowed, so my Mum made a strict rule not to leave home without shoes on. That's just my experience of mine, and doesn't answer your question!
You obviously have an excellent Mum who cares enough to worry about you, and has also taught you to be mature enough to come to a place like this and ask for advice. I hope our suggestions can be helpful to you.