What is the correct meaning of the word "sallim" in "Allahumma salli wa sallim ‘ala al-Nabiyy Muhammad"? And does it mean that God will convey peace to the Chosen One from its speaker?

Al-Turbashti said: "Al-Salam" means safety, and it is one of the names of Allah Almighty, meaning that He is free from every flaw and defect. And the meaning of our saying, "Al-Salamu Alayka" (peace be upon you), is that you are safe from adversities. It was also said: Its meaning is, "The name of Al-Salam be upon you." Al-Nawawi said: It was said that its meaning is seeking refuge with Allah and being protected by Him, the Exalted. So Al-Salam is a name for Him, the Exalted, estimated as: "May Allah be a protector and guarantor for you." It was also said: Its meaning is safety and salvation for you.