If you approach from the mathematics side of things, building on log₁₀ is the completely obvious approach to use. If it seems unintuitive, that’s just because you don’t understand logarithms.
> the autograding test cases did not include a test using a power of 10.
That’s a pretty glaring oversight. Boundary cases are probably the most important things to cover in such tests. I’d be wanting to test things like 0, 1, 9, 10, 11, 99, 100, 101, and so forth. (Also negative numbers, unless the problem explicitly constrained it to {0, 1, 2, …}.)
We often talk about edge cases in testing, but this reveals that the edges can be not just at the extremes, but also at intermediate value changes. Put another way (still fuzzy!), these are the interesting values. You test interesting values.
This would also be a good place to use property testing; instead of hard-coding a bunch of tests (or perhaps as well as), compare against a large number of generated values, comparing with a known-good implementation, probably just len(str(number)).
The 'clever' solution fails miserably on value zero and needs hard-coding to handle it. That looks like using the wrong tool.
As for the handling of zero, well, that’s not about mathematics or about how a computer stores or represents data—that’s about how humans represent data. We choose to special-case zero, allowing it to have a leading zero which we never allow for anything else. All solutions in software will need to special-case zero.