refactor(auth): share the auth landing and extract AuthField

The login and register pages were near-identical after the previous cleanup,
and both forms repeated the same labelled, icon-prefixed input seven times.
Move the data loading and page shell into auth-landing.tsx (loadAuthLanding +
AuthLandingView) and the input markup into a single AuthField, so the pages
become thin compositions and every field shares one focus, icon and aria
implementation. The numbered section headers collapse into AuthSectionHeader.

No behaviour change.

src/components/auth/auth-field.tsx

@@ -0,0 +1,106 @@
+"use client";
+
+import type { LucideIcon } from "lucide-react";
+import type { CSSProperties, ReactNode, Ref } from "react";
+
+const ICON_CLASS =
+	"pointer-events-none absolute left-3.5 top-1/2 h-4 w-4 -translate-y-1/2";
+
+export interface AuthFieldProps {
+	id: string;
+	name: string;
+	label: string;
+	icon: LucideIcon;
+	type?: string;
+	/** Controlled value; omit both `value` and `onChange` for an uncontrolled field. */
+	value?: string;
+	onChange?: (value: string) => void;
+	placeholder?: string;
+	autoComplete?: string;
+	inputMode?:
+		| "none"
+		| "text"
+		| "tel"
+		| "url"
+		| "email"
+		| "numeric"
+		| "decimal"
+		| "search";
+	required?: boolean;
+	disabled?: boolean;
+	/** Marks the field with `aria-invalid` and a danger border. */
+	invalid?: boolean;
+	/** id of the element describing this field (e.g. an error banner). */
+	describedBy?: string;
+	iconColor?: string;
+	inputStyle?: CSSProperties;
+	/** Absolutely positioned control inside the input, e.g. `PasswordToggle`. */
+	trailing?: ReactNode;
+	/** Content rendered below the field: strength meter, policy hints, mismatch. */
+	children?: ReactNode;
+	/** Extra classes on the wrapping `space-y` container. */
+	className?: string;
+	inputRef?: Ref<HTMLInputElement>;
+}
+
+/**
+ * One labelled, icon-prefixed auth input. Login and register repeat this markup
+ * seven times; centralising it keeps the icon, focus and `aria-describedby`
+ * behaviour identical everywhere.
+ */
+export function AuthField({
+	id,
+	name,
+	label,
+	icon: Icon,
+	type = "text",
+	value,
+	onChange,
+	placeholder,
+	autoComplete,
+	inputMode,
+	required,
+	disabled,
+	invalid,
+	describedBy,
+	iconColor = "var(--color-text-muted)",
+	inputStyle,
+	trailing,
+	children,
+	className = "",
+	inputRef,
+}: AuthFieldProps) {
+	return (
+		<div className={`space-y-1.5 ${className}`}>
+			<label htmlFor={id} className="auth-label">
+				{label}
+			</label>
+			<div className="relative">
+				<Icon
+					aria-hidden="true"
+					className={ICON_CLASS}
+					style={{ color: iconColor }}
+				/>
+				<input
+					ref={inputRef}
+					id={id}
+					name={name}
+					type={type}
+					value={value}
+					onChange={onChange ? (e) => onChange(e.target.value) : undefined}
+					placeholder={placeholder}
+					autoComplete={autoComplete}
+					inputMode={inputMode}
+					required={required}
+					disabled={disabled}
+					aria-invalid={invalid ? true : undefined}
+					aria-describedby={describedBy}
+					className={`auth-input has-icon ${trailing ? "has-action" : ""}`}
+					style={inputStyle}
+				/>
+				{trailing}
+			</div>
+			{children}
+		</div>
+	);
+}