How do TVSS and Circuit Breakers (thermal-magnetic) interact with each-other?
Breakers are for overcurrent. TVSS is for overvoltage. They protect against different aspects of different things. They have nothing to do with each other.
Lightning already traveled thousands of feet through the air. The little air gap in a circuit breaker isn't going to do anything to stop the lightning even if it were fast enough, which its not.
Series breakers don't increase protection (in that protection doesn't increase by stacking breakers). They just let you tailor protection for different parts of the system. Each breaker is protecting something known at the time of installation in the system from igniting, but downstream current-handling capability and loads are unknown and could be much smaller. So if you want to protect specifically for those loads you add breakers that trip sooner in series specifically for that load. It also lets only part of the system trip without bringing down everything, and allows you to shutdown part of the system for maintenance without bringing down the whole system.

In your example, you have a main panel leading to a secondary panel. Just one secondary panel? Or multiple secondary panels? If multiple secondary panels, the current capability of those panels is probably less than the main panel which means the main panel would have a larger breaker since it must carry all the current, while the secondary panels have smaller breakers since they only carry a fraction of the current running through the main panel.
So if something goes wrong downstream of the secondary panel, only that panel trips and it trips at a value low enough to protect that panel. If it was the main panel that had to trip, the secondary panel would be long gone and on fire since the main panel would only trip if the secondary panel passed the same current that the main panel was expected to trip at.
If something goes wrong within the main panel or itself or after the main panel but before the secondary panel, then the main panel trips. The breakers secondary panels could have never protected against that something happening upstream of them.