This is only a law ending the misclassification of a job as being a contractor when they really aren’t. It doesn’t say that employers have to do any of the kinds of things you are imagining. Thus,
Uber and Lyft and other companies will still be free to hire independent contractors if they choose - but those people will really have to be independent contractors (i.e. be in that business, set their own hours, take money directly from clients, and be independent in terms of which jobs they choose to take) and
If they want to hire people who aren’t independent contractors then they have to classify them as employees and meet the rules and protections employees have. Uber and Lyft and other companies will still be free to treat every single one of these people exactly as they are now with respect to all of the issues you raise. They will just have to pay social security, and follow other rules of employment that protect employees - many of which don’t apply in the type of part time work you are describing.