What is the ruling on an individual praying at home when performing the obligatory prayer immediately after waking up, without going to the mosque?

What you mentioned is not an excuse that permits delaying prayer from the congregation. Rather, it is obligatory to hasten to it with the Muslims in the houses of Allah. Rest and eating should then follow. What you mentioned is not a legitimate excuse; rather, it is from the deceptions of Satan and the soul that incites evil, and from the weakness of faith and the lack of fear of Allah. Beware of your desires, your Satan, and your soul that incites evil, so that you may praise the outcome and achieve salvation and happiness in this world and the hereafter.