[duckdb/#19546] - Add Profiler output to logger interface needs documentation

See https://github.com/duckdb/duckdb/issues/19546

Start by reading the linked DuckDB issue #19546, since this issue names no files, tests, or documentation entry point. Identify which profiler and logger behavior the upstream issue requires documenting, then locate the corresponding page in duckdb-web. Done means the requested behavior is documented clearly and the site’s documentation checks pass.

Written by the indexing model from the issue text.