If I apply for a business credit card like cap1
Do I get a chance for bigger credit lines than personal CC?
Not necessarily; the maximum lines are almost always larger (very very few individuals in this world can possibly keep up as a consumer with real business spend) but your starting line may not even be as large.
My business CC's with Chase are dwarfed by my personal ones from them... and honestly the rationale I hear on the forums for outsized lines don't apply anyway since the majority don't report to personal credit so utilization /shrug.
Most business are small and / or fail, and these days it doesn't require a ton of capital to get a lot of business ideas off the ground... as such there isn't as much call for large lines out the gate anymore especially when we're talking sole proprietorships. If you have a business idea and are putting 10-100m into it or whatever, that's a zebra of a different stripe when talking commercial banking.
Capital One reports to your personal and business reports, correct?
Correct, just like State Farm, Discover and TD Bank for instance.