Have you talked to your manager about this, or to other managers (adjacent teams or next level up) in your current company? Ask for their guidance: What are they looking for in general in a "senior" role; which improvement areas do they see for you specifically?
As you state, expectations will vary from company to company. Assuming that a promotion at your current workplace is one option to get to senior level, why not ask them about their expectations? Also, it can't hurt to make your boss aware of your ambition.