Split a commit into multiple

I accidentally bundled unrelated changes into a single commit that touches the billing code and the README. Split that commit into two: leave the billing changes in one commit with a clear message and move the README edits into a separate commit, keeping the original author and timestamp, and stop so I can review the new commit messages before finishing.

Before I split this mixed commit, make the review easy: list exactly which changed files and hunks will go into each new commit, suggest succinct commit messages that explain why each change belongs together, and flag any dependent lines (like imports or formatting) that could cause tests to break when separated.

I just committed a bugfix and some documentation tweaks together and pushed to the feature branch. I'm afraid splitting the commit will confuse the reviewer and could change the bugfix context. I don't know if CI will rerun differently after I rewrite. What's the safest step to split and push without upsetting the PR history or losing reviewers' context?

We keep seeing commits that mix code changes and nonfunctional tweaks, then spend time splitting them later. It's slowing reviews and causing revert mistakes. Which practical habit should we adopt in day-to-day work to reduce mixed commits, and how do I enforce it without adding tedious rules?