Structured logging across Backend.AI components

Introduce structured logging across Backend.AI components (machine-parseable log records with consistent fields/context) to improve observability and log querying. Scope and format defined by the BEP.\n\nRelated existing work: BA-3718 (Error Log Service Layer), BA-4231 (Batched Logging System), BA-6106 (BraceStyleAdapter f-string cleanup).

JIRA Issue: BA-7025

Start by locating the BEP that defines the structured log format and scope, then review the related work BA-3718, BA-4231, and BA-6106. Map which Backend.AI components are in scope and verify that their records expose consistent machine-parseable fields and context; completion requires coverage across the defined scope.

Written by the indexing model from the issue text.