RC: Add process tags to remote configuration payloads

[wantsui]

What does this PR do?

Adds process tags to the dynamic instrumentation payloads, similar to these two PRs:

• chore(rc): add process tags dd-trace-py#15298
• Add process tags as list to remote config payload dd-trace-java#8705

Note In both of those the remote configuration payload required the process tags to be an array so there's now a new method in Process.rb to do this.

Motivation:

For https://datadoghq.atlassian.net/browse/AIDM-257

Change log entry

None.

Additional Notes:

Note: This PR should not be merged until #5110 gets merged

How to test the change?

I've been running:

docker compose run --rm tracer-3.3 /bin/bash
bundle exec rspec spec/datadog/core/remote/client_spec.rb
bundle exec rspec spec/datadog/core/environment/process_spec.rb

[pr-commenter]

Benchmarks

Benchmark execution time: 2025-12-16 15:45:07

Comparing candidate commit 02fc9d8 in PR branch add-process-tags-rc with baseline commit f19d88e in branch master.

Found 0 performance improvements and 0 performance regressions! Performance is the same for 44 metrics, 2 unstable metrics.

[marcotc]

Looks good, with @p-datadog's suggestion implemented.

[datadog-datadog-prod-us1]

✅ Tests

🎉 All green!

❄️ No new flaky tests detected
🧪 All tests passed

🎯 Code Coverage
• Patch Coverage: 100.00%
• Overall Coverage: 95.23% (-0.00%)

View detailed report

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[Strech]

I would like to suggest a tiny change