collab: Setup database for LLM service (#15882)

This PR puts the initial infrastructure for the LLM service's database
in place.

The LLM service will be using a separate Postgres database, with its own
set of migrations.

Currently we only connect to the database in development, as we don't
yet have the database setup for the staging/production environments.

Release Notes:

- N/A

crates/collab/src/llm/db/tests/provider_tests.rs

@@ -0,0 +1,30 @@
+use std::sync::Arc;
+
+use pretty_assertions::assert_eq;
+
+use crate::llm::db::LlmDatabase;
+use crate::test_both_llm_dbs;
+
+test_both_llm_dbs!(
+    test_initialize_providers,
+    test_initialize_providers_postgres,
+    test_initialize_providers_sqlite
+);
+
+async fn test_initialize_providers(db: &Arc<LlmDatabase>) {
+    let initial_providers = db.list_providers().await.unwrap();
+    assert_eq!(initial_providers, vec![]);
+
+    db.initialize_providers().await.unwrap();
+
+    // Do it twice, to make sure the operation is idempotent.
+    db.initialize_providers().await.unwrap();
+
+    let providers = db.list_providers().await.unwrap();
+
+    let provider_names = providers
+        .into_iter()
+        .map(|provider| provider.name)
+        .collect::<Vec<_>>();
+    assert_eq!(provider_names, vec!["anthropic".to_string()]);
+}