How important is it to have a mentor?

Important for what?

Depends on a lot of things.

The bigger and more complex the project, the more important a mentor to onboard, collaborate, and gain experience.

The better the mentor, the more you can gain in terms of specific and broad knowledge, not only about the things at hand, but understanding of alternatives and concepts.

I think it will also depend on where you're at in your programming maturity. As a student, I had a fair grasp of programming concepts, so at my co-op, I had a mentor who would review my PRs, suggest his changes, and critique both his code and my code, which really felt like a game changer at the time even though it's such a small gesture. If I wasn't as comfortable with development then as I was, I don't think a mentor would've suited me at all.

Of course, this rides on you having the (RARE) opportunity of learning under a decent mentor

Depends on what kind of mentor. A lot of times, having someone who knows tips and tricks or has seen the problem before can be really helpful. Even just watching how someone else does it can be helpful.

For example, at work we have tests written in C in the 90s to 2000s to control equipment and test our products. The way some of the new test engineers and interns would fix things would be to change a parameter and recompile the test, instead of adding a variable to the watch window, using breakpoints, stepping through functions, etc. Showing them that those tools existed was huge for troubleshooting problems whenever something breaks (which is often).

The bad kind of mentor is one who doesn't/cant explain why doing it one way may have tradeoffs as opposed to the way you would do it. Their job is to 1) set an example for good practices and 2) guide you when you are doing something in a less efficient or self sabotaging way.

It's beneficial, just looking at workflows or tools that others have often leads to multiple a-ha moments.