No, labor laws in most of the US do not require posting any positions, much less every individual position. (Civil service may require posting civil service positions individually, or at least explicitly identifying the individual positions being hired under a combined posting, and labor agreements may specify requirements for how and where union-represented positions are posted.
> They can't just have one generic position to cover many
Yes, they can.
> That would open the doors for bad hiring practices and just picking anyone you want (without proper due diligence) rather then the best candidate possible.
Bad hiring practices are not generally illegal; those that are (racial discrimination, for instance) are prohibited directly rather than by prohibiting things that might open the door for them.
I don't think (but I could be wrong) that requires separate, per position postings or even publicizing the number of positioms: if you publicize for a general job description and can't get adequate American candidates the openings for that position, that can, again AFAIK, satisfy that part of the requirement.
You apply as a SWE or SRE. Then you basically either pass their hiring bar or not. If you pass, they find out what you are interested in, what you would be a good fit for, and what team is interested in having you.
There are exceptions of course, for specialized positions or knowledge. Or if they have big gaps to fill they might do targeted recruiting for them.
I don't see why it would run awful of labor laws. They have a very structured hiring process, it doesn't allow much room for "picking anyone you want". If you pass they find a job for you.
Also, you are not required to show that you picked the best candidate possible, just that you didn’t discriminate against someone on the basis of protected categories.