Do today's junior NCOs have all the necessary tools and backing from their leadership to properly instill good order and discipline?

This would depend on the local unit. I believe that all the tools are available. The backing varies between different commands

The tools are provided. What the young NCOs do with them however is very much dependent on the way companies are run.
For decades, I had and subsequently burned into others the value of solving problems at the lowest level. Not hazing. Not tyranny. Just doing what needs to be done. At my level, I should be guiding and advising, occasionally providing resources when needed. In my house, my NCOs have all the support they need, and when they get off the rails, I rein them in and guide them back on the right track. In turn, I expect them to do the same with their Soldiers.
It isn't magic, just engagement.

I don't believe we have the backing or support anymore maybe years ago but in this present time I would say no. Today's soldiers lack's the basic discipline and integrity and we as NCO hands are tied when it comes to instilling that discipline. We place too much emphasis on these soldiers complaining and feelings. These soldiers have too much say nowadays soldiers coming straight out of basic is telling you they are not doing this and not doing that last time I checked that was not an option when I joined when did that change