Not really. The First season includes the entire main first game and all main missions. That was free on PS+, epic games, etc. There was a GOTY edition which included the season pass, which was basically a DLC that added some costumes and the Patient Zero Campaign, which added four missions to the game, it created two or three "side levels" that reused assets from Sapienza and Marakkesh but respun them into new levels in night mode. They aren't part of the main line story and not playing them will not really change your experiences going into Hitman 2 or Hitman 3.
What I'd just suggest is buying Hitman 2 gold ($20 on PSN), and then deciding whether you want to play NOW a bit or wait until Hitman 3 is released and play it all inside that engine. Really totally up to you. I had 100%'d the game on xbox but playing on PS5 now so I rebought Hitman 2 gold last week, imported the First Season into it, and have been playing 1 level a night starting with Hitman 1. Just hit the Hitman 2 level last night, still 2 weeks till Hitman 3 releases. When Hitman 3 is out I can import all my levels/progression into Hitman 3, and delete Hitman 2 (which has all the H1 levels too).
After you get a few dozen or more hours of Hitman, in whatever order you want, you can decide later if you want to spend another $10 on basically adding 4 missions to the Hitman 1 levels by paying $10. They are neat, like one is revisiting Sapienza which has been transformed into a scifi movie set, but they are entirely side, "not important" missions.
