After a clean install, did a Dell driver website check, it said all my drivers were up to date.
I don't think is possible, as I usually have to update drivers after a clean install.
Below there was a list of drivers which could be updated and recent release dates.
Can the scan be wrong, should I update drivers manually?
Where is the software that you download to the laptop that keeps an eye on drivers and performs regular clean-ups, can't find it anywhere.
The software you're looking for is called Dell Update or Dell Command Update. The latter is targeted at businesses since it supports centralized management, but it can be used standalone as well. Normally it's listed in the Drivers and Downloads section of just about every system model, but you could also just Google it and pick a result hosted on Dell.com. The system model doesn't matter, and it'll update itself on installation.
I've never used the little Web-based checker on support.dell.com. I always just select my system model and browse for available updates sorted by release date. I deliberately do NOT enter my Service Tag because sometimes that causes some updates that apply to your system to be hidden. I'd rather see everything, including updates that may not apply, than miss some things that might.