How to create a career-development plan?

I want to eventually get to VP/CTO level, which path is better? I have seen people switch to Engineering Manager for faster promotions

The role of CTO varies a lot by company (sometimes it's used by the founder to have a technical voice, without actually having management responsibility). Focusing on the VP Eng role, management is definitely a pre-requisite. If you haven't been a manager before, now is a great time to try it given your seniority.

I wouldn't say that management is an easier job than IC work, but you're probably right that (all else being equal), it'll be easier to get promoted as a manager simply because your scope grows as your team grows. You don't need to demonstrate technical brilliance in the way a very senior dev may have to.

Are there any good tips to have that discussion with my manager and set expectations (is that even a good idea?)

I do think it's a good idea to communicate your short + long term goals to your manager. However, I'd be weary of saying something like "I want to be CTO" unless you have reason to believe you may actually get that role at some point within 5 years. At the executive/CTO level, it's very hard to plan for an opportunity, so your manager probably can't help you, and in fact it may lead to them thinking that you don't have a future at the company.

Instead, I'd phrase the conversation as, "In the next 6 months - 1 year, I'm keen to learn more about management and have more impact through others. Based on my understanding of the roadmap, here are some projects where I feel I could do that, what do you think" (or replace with w/e your goal is)

Is there a way I can break up the goal into smaller achievable goals that I can make progress towards every year

Yes, definitely, and I'd encourage you to have some sort of concrete, written-down growth plan with your manager. The most obvious thing that comes to mind as a development plan for you would be people management, or at least broader technical influence. You said "I love development and solving problems using code", so the natural question will become if you can scale your impact by enabling other people to write code rather than you writing code.

So the question becomes how to build that influence/direction, and you can figure out with your manager what that looks like. Lots of options to consider: eng management, revamping the onboarding process, being part of a company tech committee/counsel, presenting at a conference, etc.