fix(auth): the two links sent by email now go somewhere

An invite has always emailed `/invite?token=…` and "Glemt adgangskode?"
has always emailed `/reset?token=…`. Neither address existed. The Go
binary serves the app shell for anything it does not recognise, the shell
found no session, and both links opened the plain sign-in form — asking an
invited person to log into an account that did not exist yet, and asking
somebody who had forgotten their password for their password.

Both APIs were finished. `POST /auth/signup` takes the invite token, reads
the email address off the invite rather than the form — so a link cannot
be redirected to somebody else — creates the account, accepts the invite
and starts the session, all in one transaction. `POST
/auth/password/reset` takes the reset token and ends every session the
account had. Nothing was missing but two pages.

They are branches of SignIn rather than screens of their own, which is
what that component already says it is for: one decision tree, so a person
is never redirected mid-authentication. The routes exist because a link
has to be an address, and each renders the same component; it reads the
token out of the URL itself.

The reset does not sign you in afterwards. The whole point of ending every
session is that somebody may have been in the account, and quietly opening
a new one here would undo the half of that which matters.

Two states that are easy to leave out, and both are reachable in one click
from an old email: a link with no token says so instead of showing a form
that cannot succeed, and a link opened while already signed in as somebody
else offers to log out rather than creating a second account for a person
who is right there in the first one.

The smoke test walks the whole invite: share a project, read the link out
of the panel that shows it when there is no mail server, open it in a
second browser context, create the account, and find the shared project in
the sidebar. A second context and not a second page — inheriting the
session would test the one case that never happens, which is what it did
on the first run.

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

web/e2e/smoke.spec.js

@@ -361,6 +361,90 @@ test('en opgave kan trækkes til en anden dag og videre til et projekt', async (
 	expect(trouble).toEqual([]);
 });
 
+/**
+ * An invite link creates the account it was sent to.
+ *
+ * The server has emailed this URL since invites were built and nothing rendered
+ * for it: the SPA fallback served the shell, the shell found no session, and the
+ * recipient got a plain sign-in form for an account that did not exist yet. A 200
+ * all the way down — the same shape as `/mcp` and `/.well-known/`, and invisible
+ * to every test that does not open the link.
+ *
+ * A second browser context, because the invitee is a different person: inheriting
+ * the signed-in session would test the one case that never happens.
+ */
+test('et invitationslink opretter kontoen og giver adgang til projektet', async ({
+	browser,
+	page
+}) => {
+	const trouble = watchForTrouble(page);
+	await page.goto('/');
+
+	const sidebar = page.getByRole('navigation', { name: 'Hovedmenu' });
+	await sidebar.getByRole('button', { name: 'Nyt projekt' }).click();
+	await sidebar.getByLabel('Projektnavn').fill('Fælleshuset');
+	await sidebar.getByLabel('Projektnavn').press('Enter');
+	await expect(page.getByRole('heading', { name: 'Fælleshuset' })).toBeVisible();
+
+	await page.getByRole('button', { name: 'Del' }).click();
+	await page.getByLabel('Inviter via e-mail').fill('nabo@example.dk');
+	await page.getByRole('button', { name: 'Inviter' }).click();
+
+	// With no mail server the link is shown rather than swallowed, which is also
+	// the only way this test can get hold of it.
+	const link = await page.locator('.link-out code').textContent();
+	expect(link).toContain('/invite?token=');
+
+	// Explicitly empty, because a context made through the `browser` fixture picks
+	// up the project's storageState — and an invitee who is already signed in as
+	// the person who sent the invite is the one case that never happens.
+	const context = await browser.newContext({ storageState: { cookies: [], origins: [] } });
+	const invitee = await context.newPage();
+	const inviteeTrouble = watchForTrouble(invitee);
+	await invitee.goto(link);
+
+	await expect(invitee.getByText('Du er inviteret')).toBeVisible();
+	await invitee.getByLabel('Navn').fill('Nabo');
+	await invitee.getByLabel(/Adgangskode/).fill('et langt kodeord til test');
+	await invitee.getByRole('button', { name: 'Opret konto' }).click();
+
+	// Signed in, with the project they were invited to.
+	await expect(invitee.getByRole('navigation', { name: 'Hovedmenu' })).toBeVisible();
+	await expect(
+		invitee.getByRole('navigation', { name: 'Hovedmenu' }).getByRole('link', { name: /Fælleshuset/ })
+	).toBeVisible();
+
+	// One failure here is not trouble: the page loads before the account exists, so
+	// the shell's first `me()` is answered 401. That 401 is how the signed-out
+	// screen appears at all.
+	expect(inviteeTrouble.filter((t) => t !== 'GET /api/v1/auth/me → 401')).toEqual([]);
+	await context.close();
+	expect(trouble).toEqual([]);
+});
+
+/**
+ * The reset link renders its own form.
+ *
+ * The token is nonsense, so this stops at the form — which is the part that did
+ * not exist. "Glemt adgangskode?" has always sent a link to this address and the
+ * API has always accepted the token; what the link opened was the sign-in screen,
+ * asking for the password the person had just said they had forgotten.
+ */
+test('nulstillingslinket viser et felt til den nye adgangskode', async ({ browser }) => {
+	const context = await browser.newContext({ storageState: { cookies: [], origins: [] } });
+	const page = await context.newPage();
+
+	await page.goto('/reset?token=ugyldigt');
+	await expect(page.getByText('Vælg en ny adgangskode')).toBeVisible();
+
+	await page.getByLabel(/adgangskode/i).fill('et langt kodeord til test');
+	await page.getByRole('button', { name: 'Gem adgangskoden' }).click();
+
+	// And it says so rather than pretending: the token is not a real one.
+	await expect(page.getByRole('alert')).toBeVisible();
+	await context.close();
+});
+
 /**
  * The MCP connector address must not fall through to the app shell.
  *