If it's about getting initial interest at all, you want to do things that builds your brand or you can put on your resume. Write a blog, maintain a personal website, do side projects, etc.
If it's about getting past one of the screening stages, you'll want to focus more on soft skills. Voice coaches and voice therapists are a thing, and speaking in a likable way is extraordinarily under-emphasized. Similar things with body posture, confidence, and communication style in on-site interviews.
If you're getting a lot of "we like you, but not sure you're a good enough coder" then it's time to binge-solve problems in "Cracking the Coding Interview". The problems will help some with the last paragraph of issues to some extent as well.
Regularly attend Meet-ups, Conferences, and Workshops. Build-up a network of friends & industry contacts. Think of them as your personal brain-trust, guys you can tap into for guidance.