fix(integrations): Fix type/async errors in Offline tests

[lobsterkatie]

This fixes a number of longstanding types errors in the tests for the Offline integration. It also simplifies some of the async code (to avoid mixing async functions and done()) and changes a mock so it is no longer assigning to a read-only property.

Getting these fixed will help unmuddy the waters with respect to the Offline test errors which are cropping up in our TS upgrade.

[github-actions]

size-limit report

Path	Base Size (2b5be64)	Current Size	Change
@sentry/browser - ES5 CDN Bundle (gzipped + minified)	19.49 KB	19.49 KB	-0.01% 🔽
@sentry/browser - ES5 CDN Bundle (minified)	62.17 KB	62.17 KB	0%
@sentry/browser - ES6 CDN Bundle (gzipped + minified)	18.12 KB	18.11 KB	-0.02% 🔽
@sentry/browser - ES6 CDN Bundle (minified)	55.5 KB	55.5 KB	0%
@sentry/browser - Webpack (gzipped + minified)	22.6 KB	22.6 KB	0%
@sentry/browser - Webpack (minified)	79.21 KB	79.21 KB	0%
@sentry/react - Webpack (gzipped + minified)	22.63 KB	22.63 KB	0%
@sentry/nextjs Client - Webpack (gzipped + minified)	47.6 KB	47.6 KB	0%
@sentry/browser + @sentry/tracing - ES5 CDN Bundle (gzipped + minified)	25.36 KB	25.36 KB	-0.01% 🔽
@sentry/browser + @sentry/tracing - ES6 CDN Bundle (gzipped + minified)	23.72 KB	23.72 KB	-0.01% 🔽

[Lms24]

Nice work, thanks for doing this. Seems like we were quite close yesterday, right? This will help a lot the TS upgrade. I checked out the branch locally and ran the tests - all tests passed 👍