Would the Companions make the Adhan in their homes before the obligatory prayer if they prayed in congregation in the mosque?

The Adhan is prescribed for everyone. It is sunnah (recommended) for an individual and for a congregation if the Adhan has already been called in the town, and it is a communal obligation (fard kifaya). The Adhan is not tied to the mosque; rather, it is prescribed for a congregation anywhere, and for an individual even if they are far from people, based on the Prophet's (peace and blessings be upon him) saying: "When the time for prayer comes, let one of you call the Adhan for you," and Abu Sa'id's statement: "Indeed, no jinn, human, or anything else hears the extent of the Mu'adhin's voice except that it will testify for him on the Day of Resurrection." The Companions did not miss attending the mosque except for a valid excuse.