Goal: Battlefield controller able to zip around stunning casters and offering help to Assassin/fighter and Barbarian/fighter melee.

The strategy I plan on using is having my Monk run to the back and stun the biggest threat caster, so ranged can take them out easier. Next, help the Melee dps with help/proning/grappling/stunning. All the while I hope to avoid damage with superior movement and denying opportunity attacks.

I'm level 4 Genasi (earth) Monk currently and feel like I messed up by taking an ASI instead of the Mobile feat. My group plans to play to 20 and beyond, but I'm not optimizing for damage just utility and mobility. My plan is to go either 17 Monk/3 Rogue, or 20 Monk.

My question is mostly:
If I do dip into rogue, what would be the best archetype for an unarmed monk?

The one that interested me the most is Scout as I really think the Skirmisher feature is good for what I want to do as well as the free expertise.

The only restriction on my character is an RP one: No weapons, armor, or magic, but can use enchanted items.

Group: We're all level 4 currently using DnD Beyond so all material are available, and only the Gunslinger has any experience.

Healer: Cleric (Life Domain)

Ranged DPS: Ranger/Fighter/Gloom Stalker & Fighter/Gunslinger

Melee DPS: Barbarian/Fighter(Path of the Totem[Bear]) & Fighter/Rogue(Assassin)

Caster: Wizard (School of Divination)

Don't go Rogue if you don't use Sneak Attack

Most of the other features can be replicated with Ki points.

Fights are usually not longer than 3 rounds, so it is 3 Ki points per fight for disengage. This is exactly as many as you lose by spending (wasting) 3 levels on Swashbuckler.

This of course depends on the number of encounters your DM usually uses.

The main reason for a Monk to multiclass to Rogue is Sneak Arrack.

Don't take the Mobile feat either

You (and your party) should focus your fire, one dead and one alive Ogre deals half as much damage as two wounded ones.

The only good reason to run around on the battlefield is to stun as many opponents as possible.

If Stunning Strike works, the Mobile feat is not needed to avoid opportunity attacks, if not, you should stay and keep trying. The best assistance you can provide to the Rogue (besides stunning) is staying next to his target to trigger his Sneak Attack.

Scout's Skirmisher

DnD is a team sport; if the enemy can't get to you, they will just beat up your friends instead. The net outcome for your party does not change, unless your AC is significantly lower than the other's.

That should not be the case, if you did point buy.

The rogue multiclass is mostly redundant for an unarmed monk with the the Mobile feat

You seem to mainly be interested in the rogue multiclass for the class's abilities to dash and disengage. However, the Mobile feat already gives you most of what you want, without requiring a multiclass which would slow down your monk class progression. With the feat, you can "disengage" from a single enemy for the cost of one attack, which is cheap for a monk. The combination of the speed increase from the feat and the monk's Unarmored Movement ability means that by 10th level, your speed is increased by a total of 30 extra feet, which means you are effectively "dashing" every turn automatically, since you are now twice as fast as the average humanoid. And on the rare occasions that you need more than that, you can spend a ki point to dash and move another 60 feet as a bonus action.

Given all this, the rogue's Cunning Action ability and the Scout rogue's Skirmish feature are mostly redundant. Being able to dash or disengage as a bonus action at will would definitely make it easier to plan your turns, but as long as you don't mind thinking through all the mechanics, you can still accomplish most of the same things with only monk class features and the Mobile feat, and still have your bonus action available for an additional attack or flurry most of the time. And as you say, with unarmed strikes, you won't be able to take advantage of the rogue's sneak attack feature, which means that your 2 or 3 levels of rogue will do almost nothing to increase your damage output in combat. Hence, those 2 or 3 rogue levels would probably be much better spent getting you to a higher monk level instead.