How would you react to an E2 who "smart mouths" you in formation?

You stop and stare…. Let him talk and you stare. Let EVERYONE ELSE know what’s up for one would assume that everyone knows what type of time you and them are on (especially if you are getting those hands just as dirty). When that “Shipmate” is done, you say: “Apparently you didn’t understand what we will be doing… “ It may be that this new boot doesn’t know the work and effort their leaders are putting in.

Finish the formation, have first sergeant send the E2 to my office ASAP and commence what can be the worst and best part of being a leader. A monumental butt chewing that has the idiot quivering on his feet.

In the old Army Pvt Shithead would have been introduce to wall to wall counseling. Since this is the kinder and gentle Army that isn't an option I might do this:
1) Have Pvt Shithead and his sqd leader to go to my "office"
2) Inform the rest of the troop that they all have extra duty for the next 2 days and they can thank Pvt Shithead for that, ,then dismiss them
3) Explain to the Sqd leader my wishes and he is to ensure that they are carry out.
4) Inform the Pvt. that for the next week he has extra duty AND if he has a problem with that, we can see the CO to find out what he think about it
As much as I hated "mass punishment" it tend to work

Office hours! I would not tolerate blatant disrespect or risk total failure in discipline.

Well, when the SHIT BIRD awakens from his COMA ( self Defense, of course ), I would write him / her up for insubordination and make sure the charges are known as serious, all the way through the chain of command. Of course, I am an OLD SALT, and I understand, with the NEW CORPS being " WOKE " and all, I would sincerely apologize if I had in any way offended the SHIT BIRD and BEG for their forgiveness.

Pull the troop aside and tell them that they crossed the line. Depending upon the troop, give a few days a shit details and see if they get religion. If they complain, offer paperwork in lieu of AND continue giving them shit details because they could not see the wisdom of shutting up and coloring and taking more of my time. If they are a habitual dirtbag, then option 2 with no room for them to even "explain." Frankly, if they have problems affecting their comportment to the point of insubordination then tell them to go to the chaplain, on their own time and after their duties are all satisfactorily completed.

File the report have him thrown in brig and in front of board members for insubordination and dishonorable discharge cause it looks like he is gonna have a hard life and needs to learn

Had this issue before, smoked the whole squad. Ensuring that they understood why. His behavior was much better ….

WOWSERS! I started in the INFANTRY MAN and ended in the SIGNAL COPRS, first and for most if I am in charge I am in CHARGE. PUNITIVE ARTICLES 77 THRU 134 were under glass on my desk! I learned this from another Noncom "THIS AINT BURGER KING and You don't get it your way"
Times have changed since my time (RETIRED 1996) however Put the young soldier in charge of his peers and make him responsible for the task! Watch his attitude and demeanor change like the flipping of a switch. SECONDLY, counseling is TIME well spent, both positive and motivational
My last experience was the best! I was assigned as a STUDENT PLT Sgt E-5, I handed out latrine duties and this young buck told me he wasn't cleaning no urinlas so I marched into the first latrine and cleaned the urinal to the degree that I could have drank from it. Never had another problem! When I PCSED to Germany that young soldier was there and so were about 15 of the peer group. Reputation made! Several years later a young LT and wife came to visit me, she asked about the incident and was told the same story, she kissed him gently and said I know where you really get it from now! Point lead, follow, or get the hell out of the way! If you have to run to the PSG, PLT LDR , 1ST SGT, or COMMANDER you are ineffective as leader. One day soldiers lives will be in you hands for split decisions actions and WITHOUT RESPECT and Obedience to orders you are setting yourself up for FAILURE!! CONGRESS APPOINTED YOU, READ YOUR PROMOTION ORDERS. THE SECECTARY of The ARMY HAS RESPOSE SPECIAL TRUST (ECT...)
God Bless those who SERVE, HAVE SERVED AND WHO ARE SERVING TODAY!

What has the military come to? What is this individual going to do if he is sent into a combat zone and told to advance? Is he going to tell the sergeant to get someone else? Is this the type of person that is expected to defend the United States? This person should be given an article 15 at least. Let's go back to 1959, Fort Knox, and Let's see if someone would get away with this then. I did not know that it has come down to being able to pick and choose what you wanted to do in the military. Looks like we need to change some of the top leaders of the military to stop this and quit worrying about CRT and WOKE.