If Senator Biden (highest honorific that I know he's entitled to) would say something like, "if you haven't gotten the vaccine yet, please get it. It's free. If you've had COVID and recovered from it, consider getting the vaccine anyway for added protection", that's well within his "bully pulpit" rights (whether the added protection part is really true or not) and there would be no pushback. It might even work. This "you must comply" bullshit just makes everybody dig their heels in, and rightly so.
Why hasn't Harris deposed him yet? She must not want the job.