Saints Row: The Third Remastered was released exclusively on the Epic store on May 22 last year. As is frequently the way of these things that means it'll be coming to Steam on May 22 this year, a fact confirmed by the Saints Row Twitter account.
The remaster comes with all the DLC and has "enhanced visual effects, lighting and re-built character, vehicle and weapon models." The original soundtrack is unchanged, since it was already perfect. While the remaster was created first and foremost for the sake of re-releasing Saints Row 3 on PS4 and Xbox One, having increased draw distances, improved environmental textures, and new character models does make it tempting to go back to Steelport.
It's not exactly vital though, since the original version of Saints Row: The Third still looks pretty dang nice on PC. Saints Row 2 had a rougher PC port, and an official patch for it is in the works, with modder Mike 'IdolNinja' Watson (who was responsible for the Gentlemen of the Row mod) in the lead. Work has been slowed down, however, due to Watson developing cancer. You can follow his Twitter account for updates.