feat(core): Deprecate API class

[AbhiPrasad]

Trying to minimize behaviour differences until we properly refactor the transports as per Extract out transports into their own modules in #4240

[github-actions]

size-limit report

Path	Base Size (f042723)	Current Size	Change
@sentry/browser - CDN Bundle (gzipped)	21.67 KB	21.44 KB	-1.09% 🔽
@sentry/browser - Webpack	23.35 KB	23.25 KB	-0.42% 🔽
@sentry/browser - Webpack - gzip = false	82.8 KB	82.15 KB	-0.8% 🔽
@sentry/react - Webpack	23.38 KB	23.29 KB	-0.41% 🔽
@sentry/nextjs Client - Webpack	48.01 KB	47.92 KB	-0.21% 🔽
@sentry/browser + @sentry/tracing - CDN Bundle (gzipped)	29.99 KB	29.77 KB	-0.73% 🔽

[mitsuhiko]

I think this is okay but generally I think this design still makes it hard for us to make improvements later. Unfortunately the subclassing situation will always be bad for minification but quite user friendly for custom transports, so it might be acceptable to do it this way.

In Python as an example we push the original options in (there are no transport options) and the transports pull from there what they need. We should probably not change this right now, but longer term I think that might be preferable here as well.

[AbhiPrasad]

I completely agree - but we can revisit this when we examine transports more holistically later on. I kept this pattern primarily to minimize the diff and possibilities for breakage.

original options in (there are no transport options) and the transports pull from there what they need

This is the direction we should head in, actually we might be able to pull it off before the major