fix: database/sql tags not propagated from registers

[hannahkm]

What does this PR do?

Propagate tags from existing, registered configs to new drivers. Ensures that spans generated from database/sql contains custom tags that are added at registration.

Motivation

Spans were missing custom tags from registered configs.

Closes #4135

Reviewer's Checklist

• Changed code has unit tests for its functionality at or near 100% coverage.
• System-Tests covering this feature have been added and enabled with the va.b.c-dev version tag.
• There is a benchmark for any new code, or changes to existing code.
• If this interacts with the agent in a new way, a system test has been added.
• New code is free of linting errors. You can check this by running ./scripts/lint.sh locally.
• Add an appropriate team label so this PR gets put in the right place for the release notes.
• Non-trivial go.mod changes, e.g. adding new modules, are reviewed by @DataDog/dd-trace-go-guild.

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[pr-commenter]

Benchmarks

Benchmark execution time: 2025-11-20 16:41:29

Comparing candidate commit 43ac3d0 in PR branch hannahkm/fix-db-sql-tags with baseline commit 1ed7e54 in branch main.

Found 0 performance improvements and 0 performance regressions! Performance is the same for 18 metrics, 0 unstable metrics.

[mtoffl01]

lgtm, thanks for doing this

[mtoffl01]

I'm not sure how much this matters for Go, but a quick optimization here might be to only initialize cfg.tags to an empty map IF we have rc.tags to copy over. So, if len(rc.tags) > 0.

This depends on whether we expect cfg.tags to already be initialized later on, when we read from it, though.