feat(env): Update environment configuration and enhance email functionality

- Renamed DATABASE_URL to POSTGRES_URL in .env.example for clarity.
- Added SMTP configuration for email sending, including host, port, user, password, and from address.
- Updated package.json to include new dependencies for email handling and UI components.
- Modified middleware to handle public and protected routes more effectively.
- Enhanced API routes for studies to support user roles and permissions.
- Updated database schema to include invitations and user roles related to studies.
- Improved user permissions handling in the permissions module.
- Added new utility functions for managing user roles and study access.

src/components/ui/badge.tsx

@@ -0,0 +1,36 @@
+import * as React from "react"
+import { cva, type VariantProps } from "class-variance-authority"
+
+import { cn } from "~/lib/utils"
+
+const badgeVariants = cva(
+  "inline-flex items-center rounded-md border px-2.5 py-0.5 text-xs font-semibold transition-colors focus:outline-none focus:ring-2 focus:ring-ring focus:ring-offset-2",
+  {
+    variants: {
+      variant: {
+        default:
+          "border-transparent bg-primary text-primary-foreground shadow hover:bg-primary/80",
+        secondary:
+          "border-transparent bg-secondary text-secondary-foreground hover:bg-secondary/80",
+        destructive:
+          "border-transparent bg-destructive text-destructive-foreground shadow hover:bg-destructive/80",
+        outline: "text-foreground",
+      },
+    },
+    defaultVariants: {
+      variant: "default",
+    },
+  }
+)
+
+export interface BadgeProps
+  extends React.HTMLAttributes<HTMLDivElement>,
+    VariantProps<typeof badgeVariants> {}
+
+function Badge({ className, variant, ...props }: BadgeProps) {
+  return (
+    <div className={cn(badgeVariants({ variant }), className)} {...props} />
+  )
+}
+
+export { Badge, badgeVariants }