fix(profiling): allow users to add new tags after profiler initialization

[sanchda]

WIP

Checklist

• Change(s) are motivated and described in the PR description
• Testing strategy is described if automated tests are not included in the PR
• Risks are described (performance impact, potential for breakage, maintainability)
• Change is maintainable (easy to change, telemetry, documentation)
• Library release note guidelines are followed or label changelog/no-changelog is set
• Documentation is included (in-code, generated user docs, public corp docs)
• Backport labels are set (if applicable)
• If this PR changes the public interface, I've notified @DataDog/apm-tees.

Reviewer Checklist

• Title is accurate
• All changes are related to the pull request's stated goal
• Description motivates each change
• Avoids breaking API changes
• Testing strategy adequately addresses listed risks
• Change is maintainable (easy to change, telemetry, documentation)
• Release note makes sense to a user of the library
• Author has acknowledged and discussed the performance implications of this PR as reported in the benchmarks PR comment
• Backport labels are set in a manner that is consistent with the release branch maintenance policy

[github-actions]

This pull request has been automatically closed after a period of inactivity.
After this much time, it will likely be easier to open a new pull request with the
same changes than to update this one from the base branch. Please comment or reopen
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