It's interesting to see the notes of someone tackling lean who's primary occupation is SWE but has a strong background in mathematics.
For SWE, the most mature option is probably Isabelle. It's also a classical theorem prover, and it's perhaps easier to start with something that doesn't have dependent types. A cool thing is that the canonical Isabelle book [1] has been rewritten in Lean [2].
[1] http://concrete-semantics.org
[2] https://github.com/lean-forward/logical_verification_2025