The Gadgeteer

[Arkhios]

It also explicitly says "turn it into your arcane firearm", which implies it is no longer a wand/staff/rod and is now something different. It also refers to "the firearm" (no arcane) when casting spells through it. If it is still only a wand/staff/rod, why would it be "turned" into something different? The description is definitely NOT clear on this. Sage Advice is silent on this, and it must have come up before; which leaves it open to interpretation. For myself, I interpret the word firearm to mean firearm.

Okay. What are the stats for it?
It clearly cannot be the DMG's firearms-with Infuse Item, it explicitly says "See the item's description in the Dungeon Master's Guide for more information about it," yet it says nothing about that in Arcane Firearm.

Indeed. Unless you can provide an exact quote describing the statistics of an Arcane Firearm, it is not a weapon. According to DMG, these are the firearms' properties:

Firearms use special ammunition, and some of them have the burst fire or reload property.

Ammunition. The ammunition of a firearm is destroyed upon use. Renaissance and modern firearms use bullets. Futuristic firearms are powered by a special type of ammunition called energy cells. An energy cell contains enough power for all the shots its firearm can make.
Burst Fire. A weapon that has the burst fire property can make a normal single-target attack, or it can spray a 10-foot-cube area within normal range with shots. Each creature in the area must succeed on a DC 15 Dexterity saving throw or take the weapon's normal damage. This action uses ten pieces of ammunition.
Reload. A limited number of shots can be made with a weapon that has the reload property. A character must then reload it using an action or a bonus action (the character's choice).

but none of those matter if we don't know what kind of ammunition it uses, or how much damage does an Arcane Firearm do by default (and what type), or how many shots can be fired before you need to reload. And, these are just a few of the details that we are still missing for an Arcane Firearm.

By RAW, it is still a wand/staff/rod with special sigils carved into it, that is merely called an Arcane Firearm, and that you can use as a Spellcasting Focus for your Artificer Spells. Do note, that an Artificer can't normally use any of those items as a Spellcasting Focus, like wizards do. The Arcane Firearm is a "firearm" only by name and vague description, not by its function.

TBH, if I had an account, I would probably go ask from the Twit-- err, X, whether the Arcane Firearm is missing something from the description, or whether it is merely an elaborate way to describe a very unique spellcasting focus. And if it was missing the details that it was intended to transform into a weapon, what are the weapon statistics of an Arcane Firearm. Even then, if they were to give those statistics, it would be a personal ruling of a designer until they updated the rule from the book itself.

Dang it! Came in expecting a Gadget-using Cannoneer

Dagnabbit! Wouldn't that have been something!