Oh hey, I grew up playing Gran Turismo as well! I actually dug out the old Playstation 1 when I was seeing family last Christmas and we had a splitscreen session racing each other on the 1997 one. It was a blast

That kind of in-depth career mode is oddly rare in modern sim racers. A lot of them are very online PvP-focussed. And I get that, but still, it'd be nice to have more. Things that come to mind are:

• The original Assetto Corsa is a bit old now and the Content Manager and Custom Shader Patch mods are basically mandatory, BUT it is extremely flexible to mod and you can make it look exactly like a Gran Turismo game if you want. It has a career mode, but it's only a series of specific racing challenges and there's no collecting or modifying of cars
• Assetto Corsa Evo is in very early access right now, but it might just be exactly what you're looking for when it does fully come out. It's due to have a single player career mode, it looks like it's going to do some kind of car collection mechanic, and it even has honest-to-god Gran Turismo style licence tests
• Automobilista 2 does not have a career mode (yet? It's on the main menu but greyed out), but apparently a fan decided they were going to do it themselves. AMS also comes with the advantage of having much better multiplayer than Assetto Corsa if you want to play with friends; AC's multiplayer is quite limited and does not let you add AI to fill out the grid
• Grid Legends might be worth a look, but I can't tell you what it's actually like to play because I haven't tried it. I have played Dirt Rally 2 by the same devs and it does have a very GT-esque career mode. It describes itself as simcade, though, so it may just be another Forza for you depending on how it drives
• Le Mans Ultimate is a more specialised experience, of course, but it's due to get a proper in-depth career mode soon

It is a pretty dim time for the single player sim racing experience, but there's fun to be had!