Thanks for proving my point. Sanders does not want to own the means of production or abolish private property. That makes him not a socialist by the very definition you posted.
https://www.google.com/amp/s/www.forbes.com/sites/timworstall/2015/11/21/whatever-the-heck-bernie-sanders-is-talking-about-its-not-socialism/amp/
https://www.realclearpolitics.com/articles/2019/08/03/why_younger_americans_misunderstand_true_socialism_140917.html
A more accurate term for what he advocates is “The Nordic Model”: a capitalist economy with high taxes and social spending, universal single-payer healthcare, and strong environmental protections.