feat: add process tags to profiling

[wantsui]

What does this PR do?

Implements AIDM-254, which is to add process tags to the profiling payloads.

Requires https://github.com/DataDog/libdatadog/pull/1359/files to be implemented first.

Motivation:

AIDM-254

Change log entry

Add process tags to the profiling payloads.

Additional Notes:

When reviewing this, keep in mind that we need the implementations across tracers to be consistent:
Java PR: DataDog/dd-trace-java#8780
Python PR: DataDog/dd-trace-py#15226
.NET PR: DataDog/dd-trace-dotnet#7715

Open Questions:

1. Is there a concept of a "root" payload in dd-trace-rb for profiling?
2. Do I need to worry about the libdatadog process file currently in this code base? 🤔

Also do not merge this PR until #5033 is merged.

Also requires libdatadog: DataDog/libdatadog#1359

How to test the change?

bundle exec rspec spec/datadog/profiling/tag_builder_spec.rb

[github-actions]

👋 Hey @DataDog/ruby-guild, please fill "Change log entry" section in the pull request description.

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**Change log entry**

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^{Visited at: 2025-11-20 21:05:02 UTC}

[github-actions]

Typing analysis

Note: Ignored files are excluded from the next sections.

Untyped methods

This PR introduces 1 partially typed method. It increases the percentage of typed methods from 54.67% to 54.77% (+0.1%).

Partially typed methods (+1-0)

❌ Introduced:

sig/datadog/core/normalizer.rbs:12
└── def self.normalize: (untyped original_value, ?remove_digit_start_char: bool) -> ::String

If you believe a method or an attribute is rightfully untyped or partially typed, you can add # untyped:accept to the end of the line to remove it from the stats.

[pr-commenter]

Benchmarks

Benchmark execution time: 2025-11-20 21:28:02

Comparing candidate commit 4696c9c in PR branch add-process-tags-to-profiling with baseline commit 9e45ade in branch add-process-tags-to-tracing.

Found 0 performance improvements and 2 performance regressions! Performance is the same for 42 metrics, 2 unstable metrics.

scenario:profiling - stack collector (native frames - native filenames disabled)

• 🟥 throughput [-163.615op/s; -162.813op/s] or [-5.284%; -5.258%]

scenario:profiling - stack collector (native frames - native filenames enabled)

• 🟥 throughput [-163.290op/s; -161.248op/s] or [-5.275%; -5.209%]