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Autosteer? Autosteer is Tesla's lane keeping assist feature so, yes, that's included with basic AP which consists of lane keeping (Autosteer), and traffic aware cruise control.
You can't pay for FSD without either paying for AP or EAP first.
All of the above are "beta" which means "buy at your own risk" and Tesla has not been told by any court to pay for any related damages, injuries, or deaths since its first AP production in 2014 or the past 5 years.
Moderator note: to reduce confusion I have edited your thread title to remove the word “oversteer” since that word is unrelated to your question about Auto Pilot.
“Auto Steer” is the lane keeping function that has been part of all versions of Auto Pilot (EAP, FSDC, etc) since it was first released in 2015.