The Moon excursion(s) is covered somewhat in the lore. (A good read is the lore short story called ‘The-Hatch’)
During one of the more recent reincarnations of the Phoenix Project (As there have been many incarnations of the Phoenix Project over hundreds of years) when they had strong support from many national organisations there were at least 2 Phoenix Project operated missions to the Moon during the 60’s/70’s.
The purpose of those missions seemed to be to search for information around various crater sites on the moon which they believed may hold information related to a ‘Alien threat’.
The first mission Phoenix-1 appears to have been a technical success, however returned little to no valuable data, the 2nd mission Phoenix-2 met with disaster and was one of the major events that saw the Phoenix Project lose a lot of its support from government entities.
There is A LOT of information directly related to game events and the initial setting the player finds themselves with within the series of short story collections published over the years leading up to the games release, and I’d definitely recommend anyone interested in the specifics of the games story read through them. As each consists of self-contained short stories, you can actually read them slowly over time with each only taking about 10-20 minutes.
Over the years, Snapshot actually compiled a series of the short stories into E-book volumes that they made available to download, though I am not seeing them directly linking to the compiled volumes on their ‘Phoenix Archives’ page which is a shame as it was a nice move to make entire collections available to download to read locally without having to go through them individually on their website.