What is meant by the believers being witnesses over mankind?

Imām Ibn al-Jawzī (d. 597/1201) summarized the scholars' opinions in his book "Zād al-Masīr" as follows:

1. To bear witness that the prophets delivered the message to their nations. Abū Saʿīd al-Khudrī narrated that the Prophet Muḥammad (ﷺ) said: "On the Day of Resurrection, a prophet will come with his followers, and another prophet will come with one or two men, and another prophet will come with more than that. It will be said to them: 'Did you convey the message?' They will say: 'No.' Then it will be said to the prophet: 'Did you convey the message?' He will say: 'Yes.' It will be said: 'Who will testify for you?' He will say: 'Muḥammad and his nation.' So, they will testify that the prophets conveyed the message. Then it will be said: 'How did you know?' They will say: 'Our Prophet informed us that the messengers had delivered the message, and we believed him.' That is the meaning of His saying: "Thus We made you a just community that you will be witnesses over the people." (Al-Baqarah 2:143)". [ʿIkrimah and Qatādah]
2. To be witnesses for Prophet Muḥammad (ﷺ) over the other nations - the Jews, Christians, and Magians regarding the truth of Prophet Muḥammad’s message. [Mujāhid]