We would rather tell you the limits up front than have a child hit them and assume they did something wrong.
What works
Anything that prints. Loops, variables, text, maths, patterns, quizzes, working out answers. That covers most of what a beginner does in their first few months, and it is the part where the ideas live.
What does not, in a browser
Programs that reach out to another website or save a file onto the device generally will not work in a phone browser editor. We tried our own dog photo project in one and it produced no result at all, while a plain printing program ran instantly in the same editor a moment later. So that is the project's limit, not the child's.
If you want the full thing on a phone
There are proper Python apps for phones, and they can save files and use the internet the way a laptop does. On Android the common one is Pydroid 3. On iPhone there is a free open source app called a-Shell which includes Python. We have not tested those ourselves, so treat them as a direction to look in rather than a recommendation, and check what they cost before installing.