I actually have found myself with a small business making and designing headset covers to be adapters for these integrated routing. Below is a summary of what I know. It’s certainly not definitive and applies more to mainstream brands than chinese brands, but I hope it’s helpful. I also hope, I dont make too many errors here as I try and type out what i know.
The first thing to know is that there isnt a single bearing size. The bearings are sized by ID (inner diameter), OD (outer diameter), two chamfers which are denoted InnerXOuter, and by H (height).
The bearing size is going to be frame specific, so you should always check to make sure you are getting the right one. For example there OD ranges from 49.5-52mm, ID from 39.5-42mm, ACB is usually [36 or 45] X 45.
Different brands also have different designs for their headset compression rings and systems. Here is a rundown of the most common ones in no specific order. There is no compatibility across these systems unless you are using a system designed to provide it.
FSA ACR (also used by Bianchi, Merida, Orbea, and Winspace)—uses a 40mm ID, 52mm OD, 7mm H, 36x45 bearing. How far in the frameset the top of the bearing sits depends on the brand as does the resulting design of the compression ring, but generally should sit 4mm deep in the frame. However, 2.5mm depths are also common as are 1mm depths. Compression ring is alloy and ~7mm thick. This is the most commonly used system by a wide margin and there are compatible parts made by other manufacturers.
Deda DCR (used by Time, Van Rysel, Botechia, prior gen Colnago Bikes and MANY smaller brands like Standert)—uses a 52mm OD, 40mm H, 8mm H, 45x45 bearing. Compression ring is a 15-20mm deep high pressure injection molded Nylon item. Depths again can vary for specific models of bike, but most are ~4mm deep. However, Deda does make a variety of C Rings of varying heights and to fit both 45x45 and 36x45 bearings in an attempt to make their system more universal. Deda does make shims for these, but they can be hard to find. IMO, this is the system easiest to retrofit to a frame.
Token/Enve (also used by no 22 and Ventum)— uses a 52mm OD, 40mm H, 8mm H, 45x45 bearing. Compression ring is composite ~7-8mm thick. These come with a set of shims and can be a good fit if you can find them.
Acros (used by Canyon, Focus and Scott)—these solutions vary a lot but the most common uses a 42mm ID, 52mm 6.5mm H, 45x45 bearing. Compression ring design varies from nylon with metal inserts to just nylon and are <10mm thick. I would use this only with an Acros bearing because of the dimensions.
Trek— 40mm ID, 51mm OD, 6.5m H, 36x45. Compression rings and headset spacers are nearly model specific at this point, however the Domane Gen 4 alloy compression ring and spacers are considered a service part for most of the models, so their use is Trek OK with. Unless you have a burning desire to fit a trek cockpit to your bike. Its probably best to avoid for other bikes.
Specialized— 40.5mm ID, 49.5 ID, 6.5mm H 45x45 bearing, SL7/Allez sprint use an alloy compression ring, post recall this is a two part item. SL8 uses a composite ring. Both versions then use the same spacer. Their fitment varies by model again. This is again an avoid using part unless you have a perfect match in terms of bearings. The compression ring is not the right fit for non Specialized bikes and the current SL7 version is a recall fix for their specific bikes.
Cervelo— 34.1 ID, 46.9 OD, 7mm H, 45x45 bearing— These use a proprietary everything including steerer shape.
Of these only the FSA, Deda, and Enve are designed for aftermarket use with the first being the most common, and a lot of space between the use of the Deda system and the Token. There is no guarantee that these will fit on your bike without measuring width a depth gauge.
For safety you absolutely should match both the chamfer and height. Because of the way the Deda and Token systems work you can use shims inside the headset. With Deda, you can just cut delrin DUB crank spacers into a C shape and use those as well.
I personally, would be wary of using a 3d printed or generic plastic compression ring, especially if they struggle to hold preload as the injection molded engineered nylons typically used for these parts are quite a bit stronger than can be produced with 3d printing. This is a pretty important part of the bike to get right and a loose headset is one fastest ways to kill a carbon frame.
Hope this is helpful to someone and thanks for reading this novel of a post.
EDIT: I should have added that a good number of the chinese integrated bars can either fit directly to an FSA split spacer or come with a transition spacer for the FSA system, so thats a good system to use from a compatibility with bars standpoint. The Deda system is more frame compatible.