I wrote up an overview of the Davion and Lyran "combat auxiliary" units we know about from canon, at least from the two Field Manual books.
In FM: Fed Suns under the Davion Heavy Guards it describes the "Heavy Guards Auxiliary" as the melding of the 293rd Artillery with 2 battalions of heavy combat engineers to form an auxiliary regiment.
In the same book, for the 12th Deneb Light Cavalry the Auxiliary is effectively the surviving infantry and armor companies after intense combat action, before the unit has rebuilt.
The 6th Syrtis Fusiliers 184th Federation Auxiliary is made up of the RCT's artillery assets and 2 battalions of combat engineers.
The trend I'm noticing among Davion units at least, is that a typical combat auxiliary regiment is about 1 battalion of artillery and 2 battalions of combat engineers. When the term is used in other areas it's often some kind of ad hoc mixed formation of leftovers or what's available.
In Field Manual Lyran Alliance...
The 13th Donegal Guards have a combat auxiliary regiment that is described as a multi-purpose regiment that mixes light and heavy armor, with VTOLs, and artillery elements. It says these sub-units operate independently. It also includes a detachment of Engineering 'mechs. It's not clear to me if this unit is a standing longtime unit or an improvised formation of survivors. The 13th had lost almost a quarter of its troops on La Grave fighting the Falcons a few years prior. If it had been a full RCT back then, then this auxiliary regiment might be a temporary amalgamation of the surviving support arms. Something that has developed structure and perhaps even a sense of permanence over time as the 13th hasn't been fully rebuilt. Or it's possible that the 29th Donegal Combat Auxiliary has always been there, and the armor and other elements just got absorbed into it as it retained some command integrity whereas the armor regiments had been completely shattered as effective commands.
The 11th Lyran Regulars have a combat auxiliary. But it specifically says it's really just a motor pool of vehicles, hovercraft, AFVs, trucks, civilian vehicles. It says 1 company is devoted to combat support operations and the rest are just there to give the unit a pool of vehicles to work from on their unconventional missions.
The 15th Lyran Regulars have a combat auxiliary. Which it says had a massive force of heavy armor, although the Falcons had destroyed a battalion's worth. I wonder if this unit was a combined arms unit. Otherwise, I'm not sure why it didn't just carry a designation like heavy armor/Panzer/Armored Cavalry etc. If it was a combined arms unit (adding in other elements like combat engineers, artillery, VTOLs) that would help to explain the Auxiliary title.
I hope that helps. It's clearly a flexible designation with a lot of different potential uses. To the Davions when used as a permanent fixture it means artillery+combat engineers, but also occasionally a merging of surviving elements under one banner. To the Lyrans it means any combined arms assemblage of different unit types, which might fight together but is just as likely to be a paper regiment only for administrative purposes, while in practice the sub-components operate independently.
In both cases it FEELs to me like a combat auxilliary represents an attempt to create a regimental level HQ under which these sub-units operate. I can see how that might be desirable since at its core a RCT is a combination of regiments, and beneath the RCT HQ and within the brigade level HQs what you essentially have are a slew of regimental HQs. Having a regimental level commanding officer and staff has the potential to ensure that those units have a greater say in RCT affairs with some Colonel equivalent at the helm, making decisions with fellow regimental commanders.
The alternative is a potentially lesser status, where those elements are battalion size or smaller and kinda grafted organically to an RCT/brigade. But in that configuration they are one tier lower in status. Which in turn means when the Colonels and Generals get together to plan an operation, those units have no one at the table explicitly representing their interests and ideas, and highlighting their contributions to things. They are expected to follow orders without having a seat at the regimental table.
There are pros and cons to either model. Having your own regimental structure means you have greater visibility within the RCT and potentially a greater contribution to large scale operational planning and execution. On the other hand, being an artillery or combat engineering unit subordinate to either the RCT HQ or a brigade or regimental HQ of other types of assets means your unit can potentially react faster on the battlefield to provide organic support.
