Until now, there has been much speculation about how many deaths there were in WW III. Pike has made it canon that 30% of the Earth's population - between 2.1 and 2.4 billion people were killed and 600,000 species of plants and animals were eradicated.
The missing Starfleet vessel is called the USS Archer, likely named after Captain Jonathan Archer, captain of the Enterprise NX-01 in Star Trek: Enterprise (2001). There was also a USS Archer in the fleet that the Enterprise E attempted to rendezvous with in Star Trek: Nemesis (2002).
The admiral that meets Pike at his house is Rear Admiral Robert April, the first captain of the Enterprise NCC-1701, who commanded her first five-year mission.
This pilot is dedicated to the late April Nocifora, a Star Trek: Discovery (2017) producer who died of cancer in 2021.
A shuttle is identified in dialogue as the Stamets, likely named in honor of Paul Stamets, the Discovery engineer who led the development of the spore drive and who is officially declared dead by this point in time.