feat: add background information field to room model

- Add background_information field to Room database table and model
- Create database migration for the new field
- Update API schemas (CreateRoom, UpdateRoom) to handle background_information
- Integrate room context into AI summarization prompts
- Add background_information field to frontend room form
- Update TypeScript types from regenerated OpenAPI spec

The background information will be used to provide context for AI-generated
summaries, helping create more appropriate and relevant meeting summaries.

🤖 Generated with [opencode](https://opencode.ai)

Co-Authored-By: opencode <noreply@opencode.ai>

www/app/api/core/bodySerializer.ts

@@ -0,0 +1,88 @@
+import type {
+  ArrayStyle,
+  ObjectStyle,
+  SerializerOptions,
+} from "./pathSerializer";
+
+export type QuerySerializer = (query: Record<string, unknown>) => string;
+
+export type BodySerializer = (body: any) => any;
+
+export interface QuerySerializerOptions {
+  allowReserved?: boolean;
+  array?: SerializerOptions<ArrayStyle>;
+  object?: SerializerOptions<ObjectStyle>;
+}
+
+const serializeFormDataPair = (
+  data: FormData,
+  key: string,
+  value: unknown,
+): void => {
+  if (typeof value === "string" || value instanceof Blob) {
+    data.append(key, value);
+  } else {
+    data.append(key, JSON.stringify(value));
+  }
+};
+
+const serializeUrlSearchParamsPair = (
+  data: URLSearchParams,
+  key: string,
+  value: unknown,
+): void => {
+  if (typeof value === "string") {
+    data.append(key, value);
+  } else {
+    data.append(key, JSON.stringify(value));
+  }
+};
+
+export const formDataBodySerializer = {
+  bodySerializer: <T extends Record<string, any> | Array<Record<string, any>>>(
+    body: T,
+  ): FormData => {
+    const data = new FormData();
+
+    Object.entries(body).forEach(([key, value]) => {
+      if (value === undefined || value === null) {
+        return;
+      }
+      if (Array.isArray(value)) {
+        value.forEach((v) => serializeFormDataPair(data, key, v));
+      } else {
+        serializeFormDataPair(data, key, value);
+      }
+    });
+
+    return data;
+  },
+};
+
+export const jsonBodySerializer = {
+  bodySerializer: <T>(body: T): string =>
+    JSON.stringify(body, (_key, value) =>
+      typeof value === "bigint" ? value.toString() : value,
+    ),
+};
+
+export const urlSearchParamsBodySerializer = {
+  bodySerializer: <T extends Record<string, any> | Array<Record<string, any>>>(
+    body: T,
+  ): string => {
+    const data = new URLSearchParams();
+
+    Object.entries(body).forEach(([key, value]) => {
+      if (value === undefined || value === null) {
+        return;
+      }
+      if (Array.isArray(value)) {
+        value.forEach((v) => serializeUrlSearchParamsPair(data, key, v));
+      } else {
+        serializeUrlSearchParamsPair(data, key, value);
+      }
+    });
+
+    return data.toString();
+  },
+};