Is it necessary to offer condolences to the deceased's family after the funeral prayer, accompanying the bier, and burial? Is this considered part of the Sunnah, even if I do not know the deceased or their family?

The Wise Lawgiver (Allah) desired to offer condolences to the family of the deceased and has promised great reward for it, whether one knew the deceased and their family or not. There is no harm in the family of the deceased standing together and distinguishing themselves so that condolences can be offered to them.