docs: stop describing a control that was deleted, and a refusal that did not happen

The integration guide's Tier 0 step 3 - the first thing a new merchant follows
- still told them to fill in a watcher URL field, which an earlier commit had
removed from the form on the grounds that a link cannot vouch for itself. The
page it links to now states the opposite of the step. Same pattern as the last
four rounds: the fix landed on the code and one doc, and missed the sibling.

The "refuses a link your server does not recognise" claim was also false, so
the code now does the stronger thing instead of the docs being weakened to
match: if this origin actually runs a watcher and that watcher has never heard
of the invoice, the link is refused, because it is not one the merchant issued.
If the origin runs no watcher - the hosted copy on GitHub Pages - there is
nothing to have recognised it, and the page stays in link-only mode with its
warning. Distinguishing those two was the whole difficulty; /healthz answers it.

Also corrected: the adapter interface and README claimed four wallet actions
including a swap that no implementation provides; the public route returns two
more fields than the guide listed; and the video script said the wallet check
gates the pay button when it only reports.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>