💄(frontend) position the login hint dynamically next to the button

Compute the position of the login hint at render time so it is
always displayed close to the login button, regardless of the
button's placement or the current viewport size.

CHANGELOG.md

@@ -30,6 +30,7 @@ and this project adheres to
 - ⚡️(frontend) add trailing slash on the /me endpoint call
 - ⚡️(backend) refactor lobby storage to bound key lookups per room
 - ⚡️(backend) refactor presence cache to bound key lookups per room
+- 💄(frontend) position the login hint dynamically next to the button
 
 ## [1.30.0] - 2026-09-01
 

src/frontend/src/layout/Header.tsx

@@ -35,30 +35,21 @@ const LoginHint = () => {
     <div
       className={css({
         position: 'absolute',
-        top: '103px',
-        right: '110px',
+        top: 'calc(100% + 12px)',
+        right: 0,
         zIndex: '100',
         outline: 'none',
         padding: '1.25rem',
-        maxWidth: '350px',
+        width: 'max-content',
+        maxWidth: 'min(350px, calc(100vw - 2rem))',
         boxShadow: '0 2px 5px rgba(0 0 0 / 0.1)',
         borderRadius: '1rem',
         backgroundColor: 'primary.200',
-        display: 'none',
-        xsm: {
-          display: 'block',
-        },
-        sm: {
-          top: '131px',
-          right: '100px',
-          zIndex: '100',
-        },
         _after: {
           content: '""',
           position: 'absolute',
           top: '-10px',
-          right: '20%',
-          marginLeft: '-10px',
+          right: '1.5rem',
           borderWidth: '0 10px 10px 10px',
           borderStyle: 'solid',
           borderColor: 'transparent transparent #E3E3FB transparent',
@@ -171,12 +162,13 @@ export const Header = () => {
                   <>
                     <div
                       className={css({
+                        position: 'relative',
                         display: { base: 'none', xsm: 'block' },
                       })}
                     >
                       <LoginButton proConnectHint={false} />
+                      <LoginHint />
                     </div>
-                    <LoginHint />
                   </>
                 )}
               {!!user && (