[core] review and remove unused and deprecated exports

[pichlermarc]

Description

@opentelemetry/core is a package that holds some shared code that's used across many packages in this repository and the contrib repository. The package currently exports a large public API which we should reduce to improve maintainability.

This issue is considered done if the following steps are completed for each of the current exports in index.ts:

• if an export is deprecated, remove the export
• if an export is not used in any other package in this repository or in contrib repository, remove the export
• if an export is used in exactly one package - move its code to that package (do not export it from the package it was moved to)
• if an export is only used in tests in this repository, extract it to a new private package @opentelemetry/internal-test-utils
• if an export is only used in tests in the contrib repository, extract it to the contrib test utils package
• remove any code that becomes unused through this process

Some exports may not fall into any of the above categories but still may be better suited for other packages. For these, please open feature-request issues here and we'll discuss moving them as they come up.

Additional Context

• contrib repo
• list of exports
• Please group the changes in a way that makes PRs easier to review. See feat(core)!: remove depreacted IdGenerator and RandomIdGenerator #5309 and feat(core)!: remove deprecated InstrumentationLibrary #5308, for an example

[SehrishHussain]

Hi @pichlermarc, is this issue open for contributions?

[pichlermarc]

@SehrishHussain it is open for contributions - if you work on it, please keep PRs scoped to smaller chunks so that it's easier to review 🙂
Examples: #5309, #5308

Please let me now if you start working on it so that we don't duplicate work :)