How/where do you manage to charge this kind of rate? Are you contracting clients directly or through some agency? Also, is this for on premise or remote work? You take on full projects or augment existing teams?
$200 per hour is about $400K per year, which is around senior engineer total comp rates, https://www.levels.fyi/.
You have to ask for the rate and demonstrate that you can deliver solutions and deliver solutions.
These are mission critical systems that process and generates millions and billions in revenue. They have already spent millions of dollars and years of effort in failed attempts.
These are the companies that will pay to get their systems back on the roadmap schedule. There are big names and small names.