According to a fatwa on IslamWeb (run by Qatar’s Islamic Affairs Ministry), the nikāḥ ceremony is simply this: the man, woman, her guardian and two witnesses should gather together (this can be done over a video call if some of these people are not living close to each other). The witnesses must be respected members of the community and known to be good Muslims. The woman’s guardian says: “[woman’s name] is your wife.” The man then says: “I accept her as a wife.” That is it. They are now Islamically engaged.
From Islamic law’s perspective there is no need for anything else. But many countries pass laws that require marriages to be registered with the government, so the imams who usually oversee these ceremonies fill out forms and submit them to the government, or ask the couple to first get a civil marriage certificate before accepting to perform the ceremony. But the ceremony does not require an imam, it is just traditional to have an imam since it makes it feel official and proper. Some Muslim cultures have no conception of a nikāḥ that does not include an imam.
Isn't Nikkah actually a marriage? If nikkah is dissolved, isn't the couple going through divorce and the woman has to observe the iddah? Why call it engagement when the Quran uses nikkah to mean marriage?
Because there is a space between engagement (nikah) and marriage (consummation) that Islamic law acknowledges. If the couple separate after the nikah but before the consummation, the Quran requires the man to only pay half the alimony to the woman, while telling the woman and her family that the pious thing to do is to not accept any of the alimony (2:237). Therefore Islam makes it easy to break engagements/nikahs that have not been consummated, similar to the way in the West breaking an engagement is nowhere as serious as a divorce.
The nikah therefore is more correctly called an engagement rather than a marriage. Some cultures do not differentiate between the two, and that is fine, since to them the nikah is always immediately followed by consummation. But other cultures separate the nikah and the wedding and consider the nikah only an engagement. This too is perfectly fine and Islamic law supports them in this, and it is practiced by millions of Muslims, both Sunni and Shia.