[RPG] the point of the Battle Smith artificer’s Steel Defender having the Vigilant trait

It is up to you and your DM, but likely it would be controlled.

Iron Defender (UA 11-12):

By 3rd level, the tinkering in your free time has borne you a faithful companion, an iron defender. This metallic creature resembles a hound, a cougar, a bear, or another four-legged creature of your choice. It is friendly to you and your companions, and it obeys your commands.

The Iron Defender has an INT of 4. The Dragon Talk: Sage Advice on Mounted Combat admits that this is vaguely defined, so rule at your discretion. According to Jeremy Crawford, most players make the choices for their mount if it isn't an important NPC-tool of the DM.

Mounted Combat and Controlling a Mount (PHB 198):

A willing creature that is at least one size larger than you and that has an appropriate anatomy can serve as a mount

While you're mounted, you have two options. You can either control the mount or allow it to act independently. Intelligent creatures, such as dragons, act independently.

The anatomy is suitable as it resembles a four-legged creature of your choice (Gnomes are size Small see PHB 37, Iron Defenders are size medium, see UA 11) and the creature is willing (see first quote).

I would rule that the Iron Defender is not an independent creature because it already moves on your initiative and enacts most of the benefits of a controlled mount:

In combat, the iron defender shares your initiative count, but it takes its turn immediately after yours. It can move and use its reaction on its own, but the only action it takes on its turn is the Dodge action, unless you take a bonus action on your turn to command it to take one of the actions in its stat block or the Dash, Disengage, or Help action.

This is congruent with what a controlled mount does.

The initiative of a controlled mount changes to match yours when you mount it. It moves as you direct it, and it has only three action options: Dash, Disengage, and Dodge. A controlled mount can move and act even on the turn that you mount it.

Yes. Your steel defender can attack, so long as it's acting independently.

From the Controlling a Mount entry..

An independent mount retains its place in the initiative order. Bearing a rider puts no restrictions on the actions the mount can take, and it moves and acts as it wishes.

And then from the Steel Defender entry, it reads..

It is friendly to you and your companions, and it obeys your commands. .. It can move and use its reaction on its own, but the only action it takes on its turn is the Dodge action, unless you take a bonus action on your turn to command it.."

Given this, when your steel defender is acting independently, it's obeying your commands. There is no indication that commanding your steel defender and controlling your mount are the same thing.

You can control a mount only if it has been trained to accept a rider. Domesticated horses, donkeys, and similar creatures are assumed to have such training. The initiative of a controlled mount changes to match yours when you mount it.

And here is why. A steel defender hasn't been trained to know that you want it to go faster when you kick its sides, or that you want it to right or left by pulling on the reigns. The steel defender just obeys your commands, which is separate and distinct from controlling a mount.

There is also no mechanical benefit to controlling it; its initiative is already the same as yours, and it already moves as you direct you, and those are the only benefits of controlling a mount. Controlling it would only limit the actions it could take.

I heavily edited my original post because, after thinking about it, I was kind of all over the place and wanted to give a more concise, sensible answer.