When I've done this, your private/dev branch may be a series of broken commits. Then you rebase onto main, squash to one commit, and test (if necessary). So what shows up on the main branch is a single, squashed, tested commit that contains one logical unit of code (usually a feature or fix).

In this model the main branch history is "real" in that it records the sequence of changes to the production code. It's "fake" in that it doesn't record the exact sequence of fumbling steps and backtracks you took to get there. But IME the latter is usually not very useful anyway.