fix(browser): Add replay and profiling options to BrowserClientOptions (#8921)

Add 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`.

Author: Lms24

packages/browser/src/client.ts

@@ -30,7 +30,9 @@ export type BrowserOptions = Options<BrowserTransportOptions> &
  * Configuration options for the Sentry Browser SDK Client class
  * @see BrowserClient for more information.
  */
-export type BrowserClientOptions = ClientOptions<BrowserTransportOptions>;
+export type BrowserClientOptions = ClientOptions<BrowserTransportOptions> &
+  BrowserClientReplayOptions &
+  BrowserClientProfilingOptions;
 
 /**
  * The Sentry Browser SDK Client.