Quiet only the stdout UI under --json, not the log level (closes #112)

Per the decision on the issue (option 1), --json no longer implies Quiet. Folding --json into Quiet pinned the stderr log level to WARN, so prune --json gave a machine consumer no record of the local index rows it deleted. The two effects are now split: a JSON field on log.Options drives only the stdout UI-quiet in setupGlobals, keeping the JSON document clean, while the stderr log level follows --verbose/--debug again (diagnostics have gone to stderr since #82). The same coupling is removed for snapshot verify, snapshot remove and remote info; snapshot list was already decoupled.

Model: opus-4-8

TODO.md

@@ -25,6 +25,17 @@ release" is exactly the contradiction
 
 # Completed Steps
 
+- 2026-09-21: Stopped `--json` from silencing stderr diagnostics
+  ([issue #112](https://git.eeqj.de/sneak/vaultik/issues/112)). `--json`
+  used to be folded into `Quiet`, which pinned the log level to `WARN`,
+  so `prune --json` gave a machine consumer no record of the local index
+  rows it deleted even under `--verbose`. `--json` now quiets only the
+  stdout UI (the JSON document must stay clean, per
+  [issue #108](https://git.eeqj.de/sneak/vaultik/issues/108)); the stderr
+  log level follows `--verbose`/`--debug` again. The coupling was
+  removed the same way for `snapshot verify`, `snapshot remove`, and
+  `remote info`, which carried it for the same outdated reason.
+
 - 2026-09-21: Stopped `prune` from reporting a failed row count as 0
   ([issue #96](https://git.eeqj.de/sneak/vaultik/issues/96)). The seven
   `getTableCount` reads in `PruneDatabase` discarded their error, so a