Is it context aware

Yes, as long as you restrict the button for new video to logged-in user, the call is aware of that user info.
These are the data that are pass to the video window, which include user name, email and picture:

$content = [
'#theme' => 'jitsi_video_page',
'#room' => $room,
<strong>'#user' => $username,</strong>
'#link_external' => Link::fromTextAndUrl('Room link', $url),
'#attached' => [
'drupalSettings' => [
'ek_jitsi' => [
'autostart' => 0,
'domain' => $domain,
'room' => $room,
'user' => $username,
<strong>'email' => $mail,
'avatar' => $picture,</strong>
'jwt' => $config->get('ek_jitsi_jwt') ? $config->get('ek_jitsi_jwt') : '',
'menu_bar' => true,
],
],
'library' => ['ek_jitsi/video'],
],
];

Thank you for your reply. Good to hear that.

So to restrict the button for new video to logged-in user, do I have to customize the code or I can do it from the UI?

Note: I haven't used this module yet

No, the button always start a video in a new room.
But the room is random.
https://www.drupal.org/docs/contributed-modules/ek-jitsi/block →