fix(replay): Replace _waitForError with recordingMode

[mydea]

After checking what could be going wrong in #6466, one possible culprit is that we mangle properties prefixed with _. Meaning that it may break when referencing such properties from outside.

As far as I see, we do this in one place as of now - we access _waitForError. So this PR refactors this.

However, imho for a "public" API (of this class, at least), it is not a great API to have waitForError, as it is a bit abstract what that means.
So I changed this to instead be mode, which can be session or error. I think this describes better what is going on, and makes it a bit more explicit when using this etc.

[github-actions]

size-limit report 📦

Path	Size
@sentry/browser - ES5 CDN Bundle (gzipped + minified)	19.68 KB (-0.01% 🔽)
@sentry/browser - ES5 CDN Bundle (minified)	60.96 KB (0%)
@sentry/browser - ES6 CDN Bundle (gzipped + minified)	18.47 KB (0%)
@sentry/browser - ES6 CDN Bundle (minified)	54.51 KB (0%)
@sentry/browser - Webpack (gzipped + minified)	20.27 KB (0%)
@sentry/browser - Webpack (minified)	66.25 KB (0%)
@sentry/react - Webpack (gzipped + minified)	20.29 KB (0%)
@sentry/nextjs Client - Webpack (gzipped + minified)	47.29 KB (0%)
@sentry/browser + @sentry/tracing - ES5 CDN Bundle (gzipped + minified)	26.67 KB (-0.01% 🔽)
@sentry/browser + @sentry/tracing - ES6 CDN Bundle (gzipped + minified)	25.12 KB (+0.01% 🔺)
@sentry/replay ES6 CDN Bundle (gzipped + minified)	41.83 KB (+0.1% 🔺)
@sentry/replay - Webpack (gzipped + minified)	37.89 KB (+0.03% 🔺)

[billyvg]

Maybe recordMode to be more specific?

[Lms24]

l: Agree w/ Billy that recordingMode is probably a little more verbose.

Let's get this in so that we get rid of the private field. This isn't everything we have to do to fix minified CDN bundles but definitely a cleaner solution than just ignoring the private field in our terser config. Great catch!

[mydea]

👍 I changed it to recordingMode!