[db] Add context propagation for PostgreSQL via SET application_name

[mhennoch]

Add context propagation for PostgreSQL via SET application_name

Part of #2162

Adds SET application_name as a context propagation mechanism for PostgreSQL, following the pattern established for SQL Server (SET CONTEXT_INFO) and Oracle (V$SESSION.ACTION).

Why SET application_name?
PostgreSQL instrumentation already supports SQL Commenter, but it has limitations:

• Prepared statements — SQL Commenter cannot be used with named/prepared queries, as the comment is baked into the statement text and every subsequent execution carries stale trace context.
• Stored procedures — SQL comments on the outer CALL statement are not visible to queries executed inside the procedure body.

SET application_name operates at the session level and avoids all of these issues. The value is visible in pg_stat_activity and the OpenTelemetry Collector PostgreSQL receiver already parses it to extract trace context from query samples.

Note on application_name

There is ongoing discussion about whether application_name is the ideal long-term mechanism — a protocol-level approach would be better but doesn't exist today. An imperfect convention behind an opt-in flag is still useful: it unblocks users now and can help motivate database-native solutions over time.

Existing implementations

• Java (PostgreSQL): splunk-otel-java#2540
• Datadog: https://github.com/DataDog/dd-trace-java/blob/8db72c0988adb1010c1f2d6b028b93b10cd10ff2/dd-java-agent/instrumentation/jdbc/src/main/java/datadog/trace/instrumentation/jdbc/JDBCDecorator.java#L372

[XSAM]

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