Saying Salalahualihiwasalam (ﷺ)
No. it is not obligatory or mandatory. It is a prayer for the prophet. To qualify something to be obligatory we need to have an explicit injunction or inference based on the explicit injunction. In this case, we have nothing like that.
we do have a hadith
It was narrated from al-Husayn ibn ‘Ali ibn Abi Taalib (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: “The miser is the one in whose presence I am mentioned and he does not send blessings upon me.” Narrated and classed as hasan by at-Tirmidhi (3546); classed as saheeh by al-Albaani in Saheeh Sunan at-Tirmidhi.
Please see for further details : Discussion 51672