docs(web): design signup name field

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

Copilot-Session: cb465cbe-a93c-4c89-96f5-591e8f0908e3

Author: AchoArnold

docs/superpowers/specs/2026-07-23-signup-name-design.md

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+# Signup Name Design
+
+## Goal
+
+Collect a required name during Firebase email/password signup and persist it as
+the Firebase user's display name.
+
+## User Interface
+
+- Show a `Name` field only when the email form is in signup mode.
+- Keep the existing email and password fields unchanged.
+- Clear field-level and general errors whenever the user switches between sign
+  in and sign up.
+
+## Signup Flow
+
+1. Validate name, email, and password.
+2. Create the Firebase email/password user.
+3. Set the new user's Firebase profile `displayName` to the trimmed name.
+4. Update the auth store and continue through the existing success redirect.
+
+## Error Handling
+
+- An empty name produces an inline error on the `Name` field.
+- Firebase account creation and profile update errors use the existing Firebase
+  error handling path.
+- Switching form modes removes stale errors before rendering the other mode.
+
+## Validation
+
+- Add or update focused component tests if the component has an existing test
+  harness.
+- Run the web lint command and the smallest relevant web test command.