fix(auth): new users inherit the system-wide default timezone

default_timezone existed as a system setting (admin-editable, exposed
via SettingsRegistry.DefaultTimezone) but nothing read it at user
creation — the CreateUser query didn't even carry the column, so every
new user got the DB default UTC regardless. Both creation paths
(public register + admin create) now seed the user's timezone from the
setting, validated with time.LoadLocation and falling back to UTC when
unwired/empty/invalid.

Test-infra fixes surfaced by the run: TestUpdateProfileSelfEdit was
self-editing the SHARED admin (renaming it past the harness cleanup's
preserve-list, leaking a second admin row that broke the last-admin
tests) — it now edits a dedicated user with a unique name; the
last-admin tests get an ensureSingleAdmin precondition helper; the
websocket collection name is run-unique (non-test names persist in the
shared DB and UNIQUE(user_id,name) 409s on rerun).

internal/database/queries.sql.go

@@ -2003,9 +2003,9 @@ func (q *Queries) CreateUnlinkedBook(ctx context.Context, arg CreateUnlinkedBook
 }
 
 const CreateUser = `-- name: CreateUser :one
-INSERT INTO users (email, username, password_hash, first_name, last_name, theme, role)
-VALUES ($1, $2, $3, $4, $5, $6, $7)
-RETURNING id, email, username, theme, first_name, last_name, role, created_at, updated_at
+INSERT INTO users (email, username, password_hash, first_name, last_name, theme, role, timezone)
+VALUES ($1, $2, $3, $4, $5, $6, $7, $8)
+RETURNING id, email, username, theme, first_name, last_name, role, timezone, created_at, updated_at
 `
 
 type CreateUserParams struct {
@@ -2016,6 +2016,7 @@ type CreateUserParams struct {
 	LastName     pgtype.Text `db:"last_name" json:"last_name"`
 	Theme        pgtype.Text `db:"theme" json:"theme"`
 	Role         string      `db:"role" json:"role"`
+	Timezone     pgtype.Text `db:"timezone" json:"timezone"`
 }
 
 type CreateUserRow struct {
@@ -2026,6 +2027,7 @@ type CreateUserRow struct {
 	FirstName pgtype.Text        `db:"first_name" json:"first_name"`
 	LastName  pgtype.Text        `db:"last_name" json:"last_name"`
 	Role      string             `db:"role" json:"role"`
+	Timezone  pgtype.Text        `db:"timezone" json:"timezone"`
 	CreatedAt pgtype.Timestamptz `db:"created_at" json:"created_at"`
 	UpdatedAt pgtype.Timestamptz `db:"updated_at" json:"updated_at"`
 }
@@ -2039,6 +2041,7 @@ func (q *Queries) CreateUser(ctx context.Context, arg CreateUserParams) (CreateU
 		arg.LastName,
 		arg.Theme,
 		arg.Role,
+		arg.Timezone,
 	)
 	var i CreateUserRow
 	err := row.Scan(
@@ -2049,6 +2052,7 @@ func (q *Queries) CreateUser(ctx context.Context, arg CreateUserParams) (CreateU
 		&i.FirstName,
 		&i.LastName,
 		&i.Role,
+		&i.Timezone,
 		&i.CreatedAt,
 		&i.UpdatedAt,
 	)