docs(*): Migrate away from deprecated addSpanProcessor in README

[chancancode]

This migrates from the deprecated addSpanProcessor method to the constructor option in preparation for the upcoming SDK 2.0 release.

This commit migrates everything in the README.md of each package, other than that there are no runtime code changes.

Technically this is a user-facing change for users that previously followed the examples, putting it in its own PR/commit so we can label it for learna-changelog if desired (probably a good idea, in case when it comes time to publishing, this ends up being the only change).

Ref #2645 (cc @pichlermarc)

[github-actions]

This package does not have an assigned component owner and is considered unmaintained. As such this package is in feature-freeze and this PR will be closed with 14 days unless a new owner or a sponsor (a member of @open-telemetry/javascript-approvers) for the feature is found. It is the responsibility of the author to find a sponsor for this feature.
Are you familiar with this package? Consider becoming a component owner.

[david-luna]

@chancancode I've updated the PR title to pass the lint process. Thanks for your contribution :)

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 90.96%. Comparing base (1dace2f) to head (035964a).
Report is 1 commits behind head on main.

Additional details and impacted files

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  Coverage   90.96%   90.96%           
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  Files         172      172           
  Lines        8137     8137           
  Branches     1649     1649           
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  Hits         7402     7402           
  Misses        735      735           

[chancancode]

@david-luna updated the branch from the UI here, let me know if you need a proper rebase