build: migrate eslint to v10 flat config and upgrade typescript

Replace .eslintrc.json with eslint.config.js using the new flat config
format required by ESLint 10. Swap @typescript-eslint/eslint-plugin and
@typescript-eslint/parser for the unified typescript-eslint package.
Upgrade TypeScript to 5.9 and @types/node to 25. Apply automatic code
fixes: remove unused catch bindings and preserve error cause in auth
header parsing.

lib/api-functions.ts

@@ -103,7 +103,7 @@ export async function connectionRequest(
   let remoteAddress;
   try {
     remoteAddress = new URL(connectionRequestUrl).hostname;
-  } catch (err) {
+  } catch {
     return "Invalid connection request URL";
   }
 
@@ -185,7 +185,7 @@ export async function connectionRequest(
         () => true,
         () => false,
       );
-    } catch (err) {
+    } catch {
       // Ignore invalid address
     }
   }