refactor(examples): update get-profiles example to use Account::fetch_user_profile

Fixes #5902

## What this PR does

Keeps the existing `Client::send()` demo but extends it with:

- A doc comment on `get_profile` explaining the spec behaviour and the 401 
condition on  (Synapse's `require_auth_for_profile_requests`)
- A `get_profile_authenticated()` fallback using `account().fetch_user_profile()` 
which internally uses `force_auth()`

examples/get_profiles/src/main.rs

@@ -2,6 +2,7 @@ use std::{env, process::exit};
 
 use matrix_sdk::{
     Client, Result as MatrixResult,
+    reqwest::StatusCode,
     ruma::{
         OwnedMxcUri, UserId,
         api::client::profile::{self, AvatarUrl, DisplayName},
@@ -19,12 +20,18 @@ struct UserProfile {
 /// This function calls the GET profile endpoint
 /// Spec: <https://spec.matrix.org/latest/client-server-api/#get_matrixclientv3profileuserid>
 /// Ruma: <https://docs.rs/ruma-client-api/latest/ruma_client_api/profile/get_profile/v3/index.html>
+/// The Matrix spec does not require authentication for this endpoint. However,
+/// some server configurations (e.g. Synapse's
+/// `require_auth_for_profile_requests`) enforce auth to prevent user
+/// enumeration, which will cause `client.send()` to return a 401 error.
 async fn get_profile(client: Client, mxid: &UserId) -> MatrixResult<UserProfile> {
     // First construct the request you want to make
     // See https://docs.rs/ruma-client-api/latest/ruma_client_api/index.html for all available Endpoints
     let request = profile::get_profile::v3::Request::new(mxid.to_owned());
 
     // Start the request using matrix_sdk::Client::send
+    // To avoid having to deal with auth errors, you can also use
+    // account().fetch_user_profile() which handles auth correctly.
     let resp = client.send(request).await?;
 
     // Use the response and construct a UserProfile struct.
@@ -37,6 +44,18 @@ async fn get_profile(client: Client, mxid: &UserId) -> MatrixResult<UserProfile>
     Ok(user_profile)
 }
 
+/// This function calls the GET profile endpoint using the authenticated client.
+/// It should succeed even if the server requires auth for profile requests.
+async fn get_profile_authenticated(client: Client) -> MatrixResult<UserProfile> {
+    let resp = client.account().fetch_user_profile().await?;
+
+    let user_profile = UserProfile {
+        avatar_url: resp.get_static::<AvatarUrl>()?,
+        displayname: resp.get_static::<DisplayName>()?,
+    };
+    Ok(user_profile)
+}
+
 async fn login(
     homeserver_url: String,
     username: &str,
@@ -69,7 +88,23 @@ async fn main() -> anyhow::Result<()> {
     let client = login(homeserver_url, &username, &password).await?;
 
     let user_id = UserId::parse(username).expect("Couldn't parse the MXID");
-    let profile = get_profile(client, &user_id).await?;
+    let profile = match get_profile(client.clone(), &user_id).await {
+        Ok(profile) => profile,
+        Err(e) => {
+            if e.as_client_api_error()
+                .is_some_and(|err| err.status_code == StatusCode::UNAUTHORIZED)
+            {
+                eprintln!(
+                    "Authentication error: {e}. Check if the server requires authentication for profile requests. Trying to fetch profile using the authenticated client instead..."
+                );
+                get_profile_authenticated(client).await?
+            } else {
+                eprintln!("Error fetching profile: {e}");
+                UserProfile { avatar_url: None, displayname: None }
+            }
+        }
+    };
+
     println!("{profile:#?}");
     Ok(())
 }