fix(browser): Add replay and profiling options to BrowserClientOptions

[Lms24]

This PR adds missing replay and profiling options to the BrowserClientOptions interface. Previously, we only exposed these types to BrowserOptions. This led to type errors for users who directly create a client, without using Sentry.init (as reported in #8857).

While one would think that BrowserClientOptions is basically a superset of BrowserOptions (leaving aside stackparser, integrations and transport) this is in fact not the case, which IMO is the core problem here. BrowserClientOptions only inherits the base Options (which are shared between browser and node), in addition to transport options. However, changing this so that, BrowserClientOptions inherits from BrowserOptions is a breaking change, so I opted to just add the missing options to BrowserClientOptions.

Happy to change this if someone has an idea how to properly fix this without a breaking change.

Furthermore, I'm not sure how to best test this. We could simply add a unit test but having such a test without assertions feels a little awkward to me. Integration tests would probably be the better choice but ours aren't type checked.
I'll leave it untested for the time being (afaik we don't explicitly test types) but if reviewers prefer a test, I'm happy to come up with something.

closes #8857

[mydea]

this seems good enough to me, let's