Keep command output to the README's stdout and stderr rules (closes #224)

The startup banner moves from stdout to stderr, so a `completion`
script, a `config get` value and the hidden `__complete` command print
only their own output. `--quiet`, `--cron` and `--json` still suppress
it.

A failing `remote info`, `prune` or `snapshot remove` under `--json`
now reports its error on stderr. Their reporters returned early under
`--json`, so the failure reached neither stream.

`snapshot verify --quiet` writes no report. A failure is still
returned and printed on stderr, with the same exit status.

Judgement call: the banner's stream, posted on the issue for the owner.

Model: opus-5-5

TODO.md

@@ -22,6 +22,15 @@ the tag exists and is exercised; what is left is merging `next` to
 
 # Completed Steps
 
+- 2026-10-06: Made command output follow the README's stdout and stderr
+  rules ([issue #224](https://git.eeqj.de/sneak/vaultik/issues/224)). The
+  startup banner went to stdout, so a `completion` script or a
+  `config get` value started with it; the banner now goes to stderr. A
+  failing `remote info`, `prune` or `snapshot remove` under `--json`
+  printed nothing on either stream, and now reports its error on stderr.
+  `snapshot verify --quiet` printed its whole report; it now prints
+  none, and a failure still reaches stderr with the same exit status.
+
 - 2026-10-06: Made restore return an error instead of panicking on a
   malformed snapshot database
   ([issue #231](https://git.eeqj.de/sneak/vaultik/issues/231)). A chunk