feat: add clerk auth support with convex (#548)

apps/web/content/docs/cli/compatibility.mdx

@@ -59,7 +59,7 @@ create-better-t-stack --runtime workers --backend hono --database sqlite --orm d
 #### Convex Backend
 When using `--backend convex`, the following options are automatically set:
 
-- `--auth false` (Convex handles auth)
+- `--auth clerk` (if compatible frontends selected, otherwise `none`)
 - `--database none` (Convex provides database)
 - `--orm none` (Convex provides data layer)
 - `--api none` (Convex provides API)
@@ -67,10 +67,12 @@ When using `--backend convex`, the following options are automatically set:
 - `--db-setup none` (Convex manages hosting)
 - `--examples todo` (Todo example works with Convex)
 
+**Note:** Convex supports Clerk authentication with compatible frontends (React frameworks, Next.js, TanStack Start, and native frameworks). Nuxt, Svelte, and Solid are not compatible with Clerk.
+
 #### No Backend
 When using `--backend none`, the following options are automatically set:
 
-- `--auth false` (No backend for auth)
+- `--auth none` (No backend for auth)
 - `--database none` (No backend for database)
 - `--orm none` (No database)
 - `--api none` (No backend for API)
@@ -158,17 +160,30 @@ create-better-t-stack --frontend next native-nativewind
 
 ## Authentication Requirements
 
-Authentication requires:
+### Better-Auth Requirements
+Better-Auth authentication requires:
 - A backend framework (cannot be `none`)
 - A database (cannot be `none`)
 - An ORM (cannot be `none`)
 
-```bash
-# ❌ Invalid - Auth without database
-create-better-t-stack --auth --database none
+### Clerk Requirements
+Clerk authentication requires:
+- Convex backend (`--backend convex`)
+- Compatible frontends (React frameworks, Next.js, TanStack Start, native frameworks)
+- Not compatible with Nuxt, Svelte, or Solid
 
-# ✅ Valid - Auth with full stack
-create-better-t-stack --auth --database postgres --orm drizzle --backend hono
+```bash
+# ❌ Invalid - Better-Auth without database
+create-better-t-stack --auth better-auth --database none
+
+# ✅ Valid - Better-Auth with full stack
+create-better-t-stack --auth better-auth --database postgres --orm drizzle --backend hono
+
+# ✅ Valid - Clerk with Convex
+create-better-t-stack --auth clerk --backend convex --frontend tanstack-router
+
+# ❌ Invalid - Clerk without Convex
+create-better-t-stack --auth clerk --backend hono
 ```
 
 ## Example Compatibility
@@ -203,8 +218,11 @@ create-better-t-stack --frontend tanstack-router
 
 ### "Authentication requires a database"
 ```bash
-# Fix by adding database
-create-better-t-stack --auth --database postgres --orm drizzle
+# Fix by adding database for Better-Auth
+create-better-t-stack --auth better-auth --database postgres --orm drizzle
+
+# Or use Clerk with Convex (no database required)
+create-better-t-stack --auth clerk --backend convex
 ```
 
 ## Validation Strategy

apps/web/content/docs/cli/index.mdx

@@ -33,6 +33,7 @@ create-better-t-stack [project-directory] [options]
 - `--database <type>`: `none`, `sqlite`, `postgres`, `mysql`, `mongodb`
 - `--orm <type>`: `none`, `drizzle`, `prisma`, `mongoose`
 - `--api <type>`: `none`, `trpc`, `orpc`
+- `--auth <provider>`: `better-auth`, `clerk`, `none` (see [Options](/docs/cli/options#authentication))
 - `--db-setup <setup>`: `none`, `turso`, `d1`, `neon`, `supabase`, `prisma-postgres`, `mongodb-atlas`, `docker`
 - `--examples <types...>`: `none`, `todo`, `ai`
 - `--web-deploy <setup>`: `none`, `wrangler`, `alchemy`

apps/web/content/docs/cli/options.mdx

@@ -217,16 +217,24 @@ create-better-t-stack --frontend none
 
 ## Authentication
 
-### `--auth / --no-auth`
+### `--auth <provider>`
 
-Include or exclude authentication setup using Better-Auth.
+Choose authentication provider:
+
+- `better-auth`: Better-Auth authentication (default)
+- `clerk`: Clerk authentication (only with Convex backend)
+- `none`: No authentication
 
 ```bash
-create-better-t-stack --auth
-create-better-t-stack --no-auth
+create-better-t-stack --auth better-auth
+create-better-t-stack --auth clerk
+create-better-t-stack --auth none
 ```
 
-**Note:** Authentication requires both a database and backend framework to be selected. It is automatically disabled when using Convex backend or when no backend is selected.
+**Note:** 
+- `better-auth` requires both a database and backend framework
+- `clerk` is only available with Convex backend
+- Authentication is automatically set to `none` when using `--backend none` or `--database none` (unless using Convex)
 
 ## Addons
 
@@ -312,7 +320,7 @@ create-better-t-stack \
   --runtime bun \
   --frontend tanstack-router \
   --api trpc \
-  --auth \
+  --auth better-auth \
   --addons pwa biome \
   --examples todo \
   --package-manager bun \

apps/web/content/docs/cli/programmatic-api.mdx

@@ -33,7 +33,7 @@ async function createProject() {
     backend: "hono",
     database: "sqlite",
     orm: "drizzle",
-    auth: true,
+    auth: "better-auth",
     packageManager: "bun",
     install: false, // Don't install deps automatically
     disableAnalytics: true, // Disable analytics
@@ -258,7 +258,7 @@ create-better-t-stack my-app \
   --backend hono \
   --database postgres \
   --orm drizzle \
-  --auth \
+  --auth better-auth \
   --yes
 ```
 
@@ -269,7 +269,7 @@ const result = await init("my-app", {
   backend: "hono",
   database: "postgres",
   orm: "drizzle",
-  auth: true,
+  auth: "better-auth",
   yes: true
 });
 ```
@@ -286,7 +286,7 @@ const result = await init("my-app", {
   backend: "hono",
   database: "postgres",
   orm: "drizzle",
-  auth: true,
+  auth: "better-auth",
   addons: ["biome", "turborepo"],
   examples: ["todo"],
   packageManager: "bun",