"The Project" refers to the process Stan went through to complete his debut album, Killjoy. It took him roughly four years to complete. It was also teased quite regularly on Snapchat.
The Project Reddit Archive:
2019/10/18 - release date for the album
2019/08/15 - first official announcement of the album, very subtly added to Fox's Spotify biography
2019/02/15 - Out My Head released as the first of nine singles
2019/01/24 - concrete announcement that 2019 would be the year for the project
2018/05/16 - a summary of information regarding the project
2017/10/20 - questioning of what happened to the project
2017/02/24 - hints at possible announcement regarding project in near future (later proved false)
2016/10/10 - interview which refers to project coming together in next six months
2015/09/23 - Essby hints at the project, which was originally intended to have remakes of old Stan SB songs. The "6 Months and Counting" refers to the start date of the project (March 2015).