feat(logging): add .With() system identifiers to all top-level loggers

[corylanou]

Description

Add structured logging context (.With()) to all top-level loggers so every log line self-identifies its source system and subsystem. This makes debugging multi-database setups significantly easier.

Resulting log hierarchy:

Store:       system=store
  └─ DB:       system=store db=mydb.sqlite
      └─ Compactor:  system=store db=mydb.sqlite subsystem=compactor
      └─ WALReader:  system=store db=mydb.sqlite subsystem=wal-reader
      └─ Replica:    system=store db=mydb.sqlite replica=s3
          └─ Client: system=store db=mydb.sqlite replica=s3 [s3 group]
Server:      system=server

Example log output: level=INFO msg="compacted snapshots" system=store db=mydb.sqlite subsystem=compactor

Changes by tier:

• Tier 0: Fix remaining Allow store logger to be configured and update some references to slog default logger #1179 changes — 3 slog.Debug → db.Logger.Debug in verify()
• Tier 1: Store logger tagged system=store, Server tagged system=server
• Tier 1.5: DB.SetLogger() propagates store logger with db=<name> to DB and compactor; called in NewStore and RegisterDB
• Tier 2: Compactor gets subsystem=compactor, WALReader gets subsystem=wal-reader
• Tier 3: All 8 replica clients + S3 Leaser gain SetLogger() for logger propagation via anonymous interface assertion

Motivation and Context

After #1178 fixed default slog usage, log lines still don't self-identify which system/subsystem produced them. In multi-database setups, it's difficult to correlate log lines to specific databases or subsystems. This also subsumes the remaining db.go changes from PR #1179.

Fixes #1189

How Has This Been Tested?

• go build ./... — passes
• go test ./... — all tests pass (including existing store/compactor/replica tests)
• go vet ./... — clean
• Pre-commit hooks (go-imports, go-vet, go-staticcheck) — all pass

Types of changes

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (would cause existing functionality to not work as expected)

Checklist

• My code follows the code style of this project (go fmt, go vet)
• I have tested my changes (go test ./...)
• I have updated the documentation accordingly (if needed)

[github-actions]

PR Build Metrics

✅ All clear — no issues detected

Check	Status	Summary
Binary size	✅	35.91 MB (+4.0 KB / +0.01%)
Dependencies	✅	No changes
Vulnerabilities	✅	None detected
Go toolchain	✅	1.25.8 (latest)
Module graph	✅	1204 edges (0)

Binary Size

	Size	Change
Base (d514bc7)	35.90 MB
PR (1b83171)	35.91 MB	+4.0 KB (+0.01%)

Dependency Changes

No dependency changes.

govulncheck Output

No vulnerabilities found.

Build Info

Metric	Value
Build time	42s
Go version	go1.25.8
Commit	1b83171

History (3 previous)

Commit	Updated	Status	Summary
27b40e8	2026-03-11 00:18 UTC	✅	35.91 MB (+4.0 KB / +0.01%)
9cdf53a	2026-03-11 00:11 UTC	✅	35.90 MB (0.0 KB / 0.00%)
727db83	2026-03-10 03:09 UTC	✅	35.90 MB (0.0 KB / 0.00%)

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_{🤖 Updated on each push.}