do believe that the resurrection happens today, and people do not lay waiting in the grave, but that is a person choice.
There is a difference between bodily resurrection and the destination of the souls/spirits of the departed.
The passage in Timothy is talking about false preachers who were saying the resurrection had happened and that people had missed it.
The resurrection of the dead will happen when Jesus returns.
That is a general resurrection of all the dead, Christians to join Jesus, non Christians to depart forever from his presence.
What happens to the souls/spirits until Jesus returns is hotly debated.
As God and heaven is outside of time, my belief is that at death we move outside of time to an instance of judgement ending either with Jesus or being excluded.