Realistic Lego car sets containing gearboxes and engines?
LEGO sets
There are more than one set with such characteristics. While first four are from 20th century, I've included them anyway, since they are well-known and include characteristics you are interested in.
Let's begin with 8860 - Car Chassis from 1980. This model has steering, 4-cylinder engine, 3 speed transmission, adjustable seats, rear suspension, differential:

Second one is 8865 - Test Car with steering, V4 engine, 3-speed transmission, adjustable seats, 4 wheel suspension, differential,
retractable headlights:

Next is 8880 - Super Car from 1994 with 4 wheel steering, V8 engine,
4 speed synchronized transmission, 4 wheel independent suspension, 3 differentials, all wheel drive:

Then 8448 - Super Street Sensation from 1999 with steering, V8 engine, 5-speed synchronized transmission with reverse, suspension, differential:

Now moving forward to 21st century.
8466 - 4 X 4 Off-Roader is the first set from 2001 with steering, V8 engine, 5-speed synchronized transmission with reverse, suspension, 4 wheel drive:

42056 - Porsche 911 GT3 RS from 2016 has steering, rear flat 6 engine, rear wheel drive, 4-speed synchronized with reverse and paddle shifting, suspension:

42048 - Race Kart from 2016 is another, while small model, but still has 1 cylinder engine and 2-speed gearbox:

42083 - Bugatti Chiron from 2018 comes with steering, rear W16 engine, 8-speed gearbox with paddle shifting, suspension:

42110 - Land Rover Defender from 2019 with steering, in-line 6 engine, 4-speed sequential gearbox, suspension:

And the latest addition - 42115 - Lamborghini Sián FKP 37 from 2020. It has steering, V12 engine, 8-speed sequential transmission with paddle shifting, suspension:

LEGO MOCs
In case you are not limiting yourself to LEGO sets there is another option - MOCs produced by AFOLs. You can find them mostly on Rebrickable. There are a lot of creations based on real life vehicles with functions sometime (quite often for larger models) exceeding those you can find in LEGO sets. Not all of them are as sturdy as LEGO model, but that is a personal preference. Although all of them come with free/paid instructions. Here is an example of MOCs in Technic theme.

Features for sets from early days up to and including 8466 are sourced from Technicopedia. Here you can find animations and more details for each of those sets. Newer sets, sadly, have not been reviewed on Technicopedia.