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

--json was folded into Quiet, which pinned the stderr log level to WARN.
So `prune --json` gave a machine consumer no record of the local index
rows it deleted, even under --verbose: the audit records were gated off
stdout and pinned below the level on stderr.

--json now quiets only the stdout UI, keeping the JSON document clean
(issue #108); the stderr log level follows --verbose/--debug again, since
diagnostics have gone to stderr since #82. The same coupling is removed
for `snapshot verify`, `snapshot remove`, and `remote info`, which
carried it for the same outdated reason.

A test asserts `--verbose prune --json` emits the cleanup record on
stderr while stdout stays exactly one document, and that --json alone
keeps it below the level.

model: claude-opus-4-8

internal/cli/app.go

@@ -49,6 +49,11 @@ type AppOptions struct {
 // silenced — per the documented convention that --quiet suppresses
 // non-error output only. The startup banner is printed by Entry
 // before cobra parses arguments, gated by the same arg-level check.
+//
+// --json quiets the UI here too, because stdout then carries a JSON
+// document and human narration would corrupt it. Unlike Quiet it does
+// not lower the stderr log level (issue #112), so --verbose/--debug
+// still surface diagnostics alongside the document.
 func setupGlobals(
 	lc fx.Lifecycle, g *globals.Globals, v *vaultik.Vaultik, opts log.Options,
 ) {
@@ -56,7 +61,7 @@ func setupGlobals(
 		OnStart: func(_ context.Context) error {
 			g.StartTime = time.Now().UTC()
 
-			if opts.Cron || opts.Quiet {
+			if opts.Cron || opts.Quiet || opts.JSON {
 				v.UI.SetQuiet(true)
 			}
 
@@ -279,10 +284,11 @@ func RunOperation(
 // shared by the list/purge/verify/remove/remote-info subcommands:
 // resolve the config, then run op against the Vaultik instance through
 // RunOperation, reporting a failure prefixed with failMsg (suppressed
-// while suppressErrors is true, e.g. under --json). extraQuiet is OR-ed
-// into LogOptions.Quiet (e.g. --json output modes).
+// while suppressErrors is true, e.g. under --json). jsonOutput marks a
+// command whose stdout is a JSON document: it quiets the UI but, unlike
+// Quiet, leaves the stderr log level alone.
 func runVaultikApp(
-	cmd *cobra.Command, extraQuiet, suppressErrors bool,
+	cmd *cobra.Command, jsonOutput, suppressErrors bool,
 	failMsg string, op func(v *vaultik.Vaultik) error,
 ) error {
 	configPath, err := ResolveConfigPath()
@@ -297,7 +303,8 @@ func runVaultikApp(
 		LogOptions: log.Options{
 			Verbose: rootFlags.Verbose,
 			Debug:   rootFlags.Debug,
-			Quiet:   rootFlags.Quiet || extraQuiet,
+			Quiet:   rootFlags.Quiet,
+			JSON:    jsonOutput,
 		},
 	}, op, func(err error) {
 		if suppressErrors {