Is it permissible for a worshiper who joined the congregational prayer after the Imam rose from bowing in the last rak'ah to leave his prayer after the Imam’s taslim in order to join a second congregation that he heard had been established, and does the ruling differ if the first prayer was the first congregation?

If you join the prayer with the Imam, even if it is in the last Tashahhud, it is not permissible for you to break the prayer after he says the tasleem in order to join another congregation. This is because it invalidates the act of worship, and Allah Almighty says: "And do not invalidate your deeds." The Prophet, peace and blessings be upon him, said: "Whatever you catch, pray, and whatever you miss, complete." This ruling is general for every rak'ah caught, and it does not differ based on the Imam's situation. If your delay was due to an excuse, you will be credited with the reward of the congregation.