Ensure Sentry is able to initialize without DSN if Spotlight is enabled

[krystofwoldrich]

Description

As part of the requirement to make Spotlight compatible with SDKs, the SDKs should be able to initialize without a DSN if Spotlight is enabled

### 🛑  Blocked by
- [ ] https://github.com/getsentry/sentry-cocoa/issues/4620
- [ ] https://github.com/getsentry/sentry-java/issues/3981

JS already supports this https://github.com/getsentry/sentry-javascript/blob/938fe65a1bb363bf92cb35df24edea27d3d75883/packages/core/src/baseclient.ts#L322

### Tasks
- [ ] Check if JS layer can send events to Spotlight without changes on native

[lucas-zimerman]

@krystofwoldrich one thing users could try is using an invalid DSN, this way errors are sent to spotlight and no extra changes would be required on the native side