docs(site): align with LoopStore collapse and rename (D-11)

Updates loopengine.dev pages that referenced the pre-rename
LoopStorageAdapter / createMemoryLoopStorageAdapter / storage option
key. Pages already in post-rename state (packages/runtime.mdx,
packages/sdk.mdx, packages/adapter-memory.mdx, packages/
adapter-postgres.mdx, running-loops/adapters.mdx, running-loops/
create-loop-system.mdx, getting-started/installation.mdx, llms.txt)
become correct without edits via the source rename — no churn.

Updates in this commit:
- components/home/CodeTabs.tsx: homepage Run + Events snippets switch
  to memoryStore() and store option key; syntax highlighter symbol
  list updated
- content/docs/integrations/index.mdx: prose reference
  LoopStorageAdapter -> LoopStore
- content/docs/integrations/http.mdx: two prose references
  LoopStorageAdapter -> LoopStore
- content/docs/integrations/postgres.mdx: prose reference
  LoopStorageAdapter -> LoopStore
- content/docs/examples/postgres-persistence.mdx: code sample updated
  (memoryStore factory, postgresStore factory, store option key);
  trailing prose reference LoopStorageAdapter -> LoopStore

Verification
- npx tsc --noEmit: clean
- pnpm lint: clean
- pnpm build: 12/12 pages prerendered, no MDX parse errors

Surface-Reconciliation-Id: SR-002

Author: betterdataco

components/home/CodeTabs.tsx

@@ -50,13 +50,13 @@ const checked = validateLoopDefinition(definition)
 if (!checked.valid) {
   throw new Error(checked.errors.map((e) => e.message).join('; '))
 }`,
-  run: `import { createMemoryLoopStorageAdapter } from '@loop-engine/adapter-memory'
+  run: `import { memoryStore } from '@loop-engine/adapter-memory'
 import { createLoopSystem } from '@loop-engine/sdk'
 
 // assumes \`definition\` from the Define tab
 const { engine } = await createLoopSystem({
   loops: [definition],
-  storage: createMemoryLoopStorageAdapter()
+  store: memoryStore()
 })
 
 await engine.start({
@@ -74,7 +74,7 @@ await engine.transition({
   events: `// assumes \`createLoopSystem\` returned \`eventBus\` alongside \`engine\`
 const { engine, eventBus } = await createLoopSystem({
   loops: [definition],
-  storage: createMemoryLoopStorageAdapter()
+  store: memoryStore()
 })
 
 eventBus.subscribe(async (event) => {
@@ -99,7 +99,7 @@ function renderHighlighted(code: string) {
     '<span class="kw">$1</span>'
   );
   return withKeywords.replace(
-    /\b(parseLoopYaml|validateLoopDefinition|createLoopSystem|createMemoryLoopStorageAdapter)\b/g,
+    /\b(parseLoopYaml|validateLoopDefinition|createLoopSystem|memoryStore)\b/g,
     '<span class="type">$1</span>'
   );
 }

content/docs/examples/postgres-persistence.mdx

@@ -38,18 +38,18 @@ QUERY STATE ---> READ INSTANCE + READ HISTORY
 
 ```ts
 import { createLoopSystem } from "@loop-engine/sdk";
-import { createPostgresStore, createSchema } from "@loop-engine/adapter-postgres";
-import { createMemoryLoopStorageAdapter } from "@loop-engine/adapter-memory";
+import { postgresStore, createSchema } from "@loop-engine/adapter-postgres";
+import { memoryStore } from "@loop-engine/adapter-memory";
 import { Pool } from "pg";
 
 // Version A: in-memory (default local dev)
-const memoryStore = createMemoryLoopStorageAdapter();
-const memoryRuntime = await createLoopSystem({ loops: [definition], store: memoryStore });
+const memStore = memoryStore();
+const memoryRuntime = await createLoopSystem({ loops: [definition], store: memStore });
 
 // Version B: postgres (durable)
 const pool = new Pool({ connectionString: process.env.DATABASE_URL });
 await createSchema(pool);
-const pgStore = createPostgresStore(pool);
+const pgStore = postgresStore(pool);
 const postgresRuntime = await createLoopSystem({ loops: [definition], store: pgStore });
 
 // Loop definitions + transition calls are unchanged across adapters.
@@ -79,5 +79,5 @@ pnpm dev
 ```
 
 <Callout variant="info" title="Adapter pattern">
-The same contract pattern extends to `adapter-kafka` and `adapter-http`. Any backend implementing `LoopStorageAdapter` can be used.
+The same contract pattern extends to `adapter-kafka` and `adapter-http`. Any backend implementing `LoopStore` can be used.
 </Callout>

content/docs/integrations/http.mdx

@@ -11,7 +11,7 @@ section: Integrations
 
 ## What it does
 
-Implements `LoopStorageAdapter` over HTTP. Any REST service that speaks the adapter protocol can back loop state storage. This is useful for integrating with existing services or remote storage planes.
+Implements `LoopStore` over HTTP. Any REST service that speaks the adapter protocol can back loop state storage. This is useful for integrating with existing services or remote storage planes.
 
 ## Adapter protocol
 
@@ -51,7 +51,7 @@ Expected backend endpoints:
 
 ## Note
 
-If your backend is in the same process, implementing `LoopStorageAdapter` directly is usually simpler than standing up the HTTP protocol.
+If your backend is in the same process, implementing `LoopStore` directly is usually simpler than standing up the HTTP protocol.
 
 ## Configuration reference
 

content/docs/integrations/index.mdx

@@ -136,7 +136,7 @@ Connect Loop Engine to commerce platforms and LLM commerce data layers.
 
 ## Building an integration?
 
-The Loop Engine adapter interface is open and documented. Any backend that implements `LoopStorageAdapter` is valid.
+The Loop Engine adapter interface is open and documented. Any backend that implements `LoopStore` is valid.
 
 - [Adapter interface docs →](/docs/running-loops/adapters)
 - [Apply for certification →](mailto:oss@betterdata.co)

content/docs/integrations/postgres.mdx

@@ -11,7 +11,7 @@ section: Integrations
 
 ## What it does
 
-Swaps the in-memory adapter for PostgreSQL persistence. Loop state, transitions, and events are stored in Postgres through the same `LoopStorageAdapter` interface, so loop definitions and business logic remain unchanged.
+Swaps the in-memory adapter for PostgreSQL persistence. Loop state, transitions, and events are stored in Postgres through the same `LoopStore` interface, so loop definitions and business logic remain unchanged.
 
 ## Quick setup