Store and Use Refresh Token on Expiry

We've the same requirement. Our solution is to store the tokens on the user session for later use (potential token refreshing).

Hooking to the "openid_connect_userinfo_save" did the job for us:

/**
 * Implements hook_openid_connect_userinfo_save().
 */
function helbling_user_openid_connect_userinfo_save(UserInterface $account, array $context): void {
	// Store OpenID Connect tokens for later use.
	$request = \Drupal::request();
	if( ! $request->hasSession() ) {
		// This is a strange situation: login via openid connect seem to have completed though no
		// PHP session is available required to keep Drupal's login state.
		// ¯\_(ツ)_/¯
		return;
	}
	$tokens = $context['tokens'];
	$request->getSession()->set('oidc_tokens', $tokens);
}