Calendly does not manage a logged-in / logged-out state via oauth. Each request to calendly is authenticated via a unique oauth token. Each time you make a request to Calendly (whether or not a user is logged into your app) you will need to use a refresh token to acquire an access token and then use that access token to make a request. You also do not need to revoke tokens when a user logs out of your account. Access tokens are automatically revoked when they are used.

I do have revoked token when user does logout. Let me share your relevant codebase in C#.

async Task<BaseOutput<RevokeToken>> RevokeClientTokenRequestMethod(FormUrlEncodedContent content)
{
    HttpRequestMessage httpRequest = new(HttpMethod.Post, $"{UrlType.OAuth}{UrlType.RevokeToken}")
    {
        Content = content
    };
    HttpResponseMessage response = await _httpClient.SendAsync(httpRequest);
    string reponseContent = await response.Content.ReadAsStringAsync();
    if (response.StatusCode is not HttpStatusCode.OK)
    {
        AuthError error = Helper.DeserializeObject<AuthError>(reponseContent, _options);
        HandleError(error);
    }
    RevokeToken revokeToken = Helper.DeserializeObject<RevokeToken>(reponseContent, _options);
    return BaseOutput<RevokeToken>.GetOutput(revokeToken);
}

private async Task<T> ExecuteRequest<T>(Func<Task<T>> action)
{
    _httpClient.DefaultRequestHeaders.Add(
       HeaderTypeKey.ContentType,
       HeaderTypeValue.ApplicationXWwwFormUrlEncoded);
    return await action();
}

 When user connect with my application using OAuth2.0, it does store these cookies inside their calendly.com domain.
 

Hence, at the time of logging out event I revoke token of user (both access and refresh) it does again login directly.