What is the most effective way to write a growth plan?

Can you ask your manager (or whoever is requesting the plan) and colleagues for example growth plans? Any details you can gather on what they are looking for would be helpful. If you search Taro for "growth plan", you will find a good amount of posts and videos on this topic, like this one: https://www.jointaro.com/question/BG4rWlnWQamBFI9ujCni/how-do-i-create-a-growth-plan-with-my-managermentor-and-what-should-it-include/

However, since you're being asked to produce this, clarifying what the requestor wants and seeing a template or examples from your company will be incredibly useful. Submitting a generic one will be less useful. This is a great opportunity to practice communication skills and clarify ambiguity, so you can deliver a high-quality growth plan.

A lot of companies will have some criteria they use to decide whether someone is ready to be promoted. I would try to start from the end goal: what does a senior software engineer looks like at your company.

It usually boils down to project scope and influence scope. Project scope is related to how impactful your projects are to either other engineers (for example, in engineering productivity or internal tools) or to your users (for example, increasing conversion). Influence scope is related to how impactful you are to other engineers in your organization (this might be input on technical design or mentoring other engineers).

Once you have those in mind, you can brainstorm what projects or actions would get you to that scope.

David's advice is spot-on: Start with examples from other people in the company. I'm sure you aren't the 1st person ever in your company to make a growth plan for mid-level to senior.

When it comes to a growth plan overall though, the main thing is to illustrate the delta. Make it clear what it's like to go from here (mid-level engineer behavior) to there (senior engineer behavior). I talk about this extensively in our promotion course here: https://www.jointaro.com/course/nail-your-promotion-as-a-software-engineer/create-an-expectations-plan/

On top of that, I recommend breaking it down by engineering performance review axes if your company has those (I also talk about this in the course).

For mid-level to senior, I recommend our course about it as well: [Course] Grow From Mid-Level To Senior Engineer: L4 To L5