How transparent can I be with my manager?

I think you need to separate 2 things here, imposter syndrome, and manager transparency.

About the imposter syndrome, I think it's totally normal to feel this way being a new grad and a new member in the team, if this stays with you after 1 year, then you may want to address it, otherwise, just keep learning from everyone around you, and take every chance to do so.

Regarding manager transparency: IMO, it all depends on 2 things, Trust and Respect.

If you fully trust your manager, and you both have a good respectful relation, then I would be totally open with things I would not be with other managers, think looking for other opportunities, looking for outside mentors, etc... This ensures you gets a sincere advice, and makes sure he is also in the know to make sure he reaches out to hire a replacement etc.. And most importantly, it helps keeping the bridge solid.

This is a good question, but it's a tricky one. In a nutshell, the answer is "Share more if your manager likes you, less if they don't". However, you need to do the work to figure out how healthy that bond between your manager and you really is. This will require some amount of social intuition from you alongside careful observation and plenty of meetings (obviously).

It will also require some amount of a leap of faith as humans misjudge the depth of their relationships all the time - I'm sure we've all had a situation where we thought this person really deserved our trust but sadly didn't. Keep this in mind, but don't let you stop you from opening up.

Going back to your particular scenario, I think you should share your feelings of anxiety and imposter syndrome with your manager (assuming your relationship is good). This was actually how I conquered my imposter syndrome back when I started at Meta (thankfully my 1st manager there was extremely empathetic).

Here's another good thread to check out: "What's the boundary between what's okay to share with your manager vs. what's not? Are some things simply too deep?"

I like this one about imposter syndrome as well: "I've felt imposter syndrome from seeing super talented peers - How do I deal with this?"

Lastly, I just want to mention that if you play your cards right (use your 1 on 1s effectively, add value to people, communicate with empathy and enthusiasm), the ceiling on what you can share with your manager is effectively infinite.

I have had 11 managers. For the first 5+, I was pretty terrible about managing this relationship and getting the most from it. By the end, I got pretty good at it, which is a large reason behind my career success.

How good? Well, I told my manager at Robinhood that I was exiting Robinhood to start my own company 2 months before I was going to leave. That's how much I trusted her, because we got along really well. She was sad that I was leaving but supported my decision. And when Taro launched on Hacker News many, many months after I left, she even reached out to me personally to congratulate me! That's how powerful you can make this relationship.

Just because they're your boss doesn't mean you can't turn them into a friend.

In addition to Amazon's answer, I'd highly recommend going through this course from an ex-VP at Amazon: Managing Up: Build Effective Relationships With Your Boss