Yes, you got it.

It’s possible that however your ISP provided router is designed, it’s got some hidden port forward configuration. If that router has an option typically referred to as “bridge mode”, you could bypass its routing features altogether and use your own router instead.

ISPs often have clauses about using their residential internet for hosting servers or exposed services, and it’s possible your has taken a different approach to mitigating traffic from those sources.

If you can, I’d recommend using your own router rather than what the ISP provides.

If I understand correctly, it sounds like you moved from an ISP that uses CGNAT to one that does not. Does your ISP provide a modem? If so, are you relying on the software features of that modem, or do you have a router inbetween?