What's some good high-level advice to start progressing to senior engineer?

Good question! Here's 3 great resources to check out IMHO:

• Developing The Technical Proficiency Of A Senior SWE - Q&A From An Amazon SDE2
• Leading Turbulent Projects - Q&A From A Meta E4
• Finding A Multi-Million $$$ IG Bug - Story Around Creating Senior SWE Scope

I think the big mindset shift for most mid-level engineers growing to senior is that they need to expand their world view, viewing projects and teams more holistically. Most earlier mid-level engineers I've worked with only really focus on their part of the stack for their product (e.g. "I own the Android part of the ads CTA button in Instagram."). Once you start breaking out of that mental bubble, you'll find yourself influencing others and leading entire projects.