Should I recite the complete Tashahhud with the Imam in the last rak'ah if I did not join him from the beginning of the prayer, and this rak'ah is not the last one for me?

There is no disagreement among scholars that the latecomer (masbuq) should sit with the Imam during the tashahhud (testification of faith) sitting and recite the entire tashahhud, and then supplicate with whatever he can. This is due to the generality of the Prophet's (peace and blessings be upon him) saying: "Indeed, the Imam is appointed to be followed."