Composite Plating and Heavy Plating are intended to count as armor.
Keith Baker, original creator of Eberron and lead designer for the Wayfinder's Guide to Eberron, addresses this question (and many others) in the WGtE FAQ on his website:
Does the Warforged Heavy Plating Integrated Protection work with the Fighter’s Defense Fighting Style? Unclear on if (armor) means you’re “wearing armor” or not.
The intent is while you are using darkwood core you are not considered to be wearing armor for purposes of game effects such as Unarmored Defense, while you are considered to be wearing armor when you’re using one of the plating modes. However, as written Integrated Protection doesn’t allow you to benefit from the Defense Fighting Style. This won’t be changed until people have a chance to provide feedback on the race mechanics as they stand.
Baker points out that the feature doesn't specifically clarify that Composite Plating or Heavy Plating count as armor - but the parenthetical after each one reflects the intent, which is that Darkwood Core counts as being unarmored and that the other two options count as being armored. This is relevant for features like the Defense fighting style (which requires you to be armored), or the monk's Unarmored Movement feature (which, as the name implies, requires that you be unarmored).
In another response, he also says:
When a warforged is using the darkwood core (unarmored) mode and have light armor proficiency, can they choose whether they are considered to be armored or unarmored?
No. You are always considered to be unarmored when using darkwood core, and always considered to be armored when using plating.
So you can choose which of the three modes to use (depending on what armor you're proficient in), but you can't choose whether that mode counts as being armored.
...but as currently written, they don't count specifically as medium or heavy armor.
Baker also answers a related question about what kind of armor the Integrated Protection feature counts as:
Composite Plating and Heavy Plating both say “Armored” but do they count as medium and heavy armor respectively? Specifically does a warforged Barbarian in Heavy Plating mode lack access to the benefits of rage?
As written, the current version simply specifies that plating counts as armor, not that it counts specifically as heavy or medium armor. So in this version, a warforged barbarian can rage while in the heavy plating mode… though they will have to acquire the heavy armor proficiency before they can use heavy plating.
This may change in the future, but as of right now, a warforged barbarian can gain the benefits of Rage regardless of what defensive mode they're in. However, they can't benefit from features that forbid any armor at all while using Composite Plating or Heavy Plating.
"Warforged, roll out!"
The Integrated Tool feature says (emphasis mine):
Choose a tool you're proficient with. It becomes integrated into your body, and you double your proficiency bonus for any ability checks you make with it. You must have your hands free to use this tool.
So RAW this means any tool you are proficient with is eligible. So the question becomes whether something is a tool.
For the RAW, I would assume anything listed in the Tools table in the PHB (p. 154) counts, as well as anything listed in similar list in later books.
The last line of the Tools table lists "Vehicles (land or water)", so by RAW they should qualify. This is further empowered by the fact that the Sailor (PHB p. 139) and Soldier (PHB p. 140) list "vehicles (water)" and "vehicles (land)" as Tool Proficiencies respectively.
So yes, RAW vehicles could be integrated into a Warforged Envoy.
Beyond RAW
As a DM, I would rein this in a bit for instance by only allowing person-sized vehicles. So you can integrate a small rowboat or a cart or sled (PHB p. 157) - something you'd maybe able to carry 2 other people in, but not really self-powered.
Having said that, I could very easily see other DMs saying no to the idea. So if you want to actually use this feature this way, discuss it with your DM first.
So no, you could not be an integrated Air Galleon (though this might be an idea for a Knight Rider one-shot...)
Best Answer
Different AC calculations don't stack; you pick which one to use
As Slagmoth pointed out, this general topic has been asked and answered many times by the designers, and an official answer appears in the Sage Advice Compendium:
(The entry goes on to clarify that AC bonuses, like those provided by shields, do stack with AC calculations; it's simply that if your features give you different ways to calculate your AC, you pick one.)
In addition, Keith Baker - original Eberron designer, and primary author of the Wayfinder's Guide to Eberron - has posted an FAQ on his website about the Wayfinder's Guide (which he has continued to update to answer questions). It contains a section about the Integrated Protection feature, which specifically answers this question and references the Sage Advice ruling:
The section also clarifies whether the Integrated Protection feature counts as "armor"/"being armored" for other features. It's a worthwhile read.
In short: you have the choice between two different AC calculations:
or
They don't stack. You simply have the choice between one and the other (presumably you'd choose the one that gives you a higher overall AC).