Your mistaking a few terms . . . This gets complicated because the best demonstration is organizational charts, lol. I may have to grab the one in the back of . . . CM Mercs? Or was it 1SW SB that I was looking at, to fill out with the structures.
I said the dedicated FOs would not be organic to the line infantry battalions or companies. For the purposes of training artillery and FOs, they might be in the same battalion (though to be honest, I knew of the 13Cs but never had them around my MLRS unit & I was in during 2 organizational shuffles) it depends on force doctrine. We had observers for safety purposes during live fires, but during training all our FO reports were script generated.
Anyway, here is an example-
To go through left to right . . .
You have 3 HQ & HQ Support Companies for the brigade you can sea all the details of what that entails but the HQ Support is a company of military police & signal company
Recon BN is a dedicated brigade level asset, but in practice it might be broken up to have a troop assigned to each battalion or they could be tasked by BDE. Recon may also have most of the intel staff and sensors like that Target Acquisition plt- chart is less clear.
3 Maneuver BNs- each has 3 Stryker companies w/1 MGS plt, a scout platoon, and a mortar section the last 3 would fall under the BN HQ
Anti-Tank Company- BDE can either keep them together or assign platoons to Maneuver BNs
Fires (current Artillery catch phrase)- looks like 5 FO-type parties which could be with the intention of Recon, 3 Manuever & Anti-Tank each getting one but they are part of the arty BN. Not sure why they picture Towed as the icon is for Self-Propelled which matches their movement. This is a BDE level asset.
Engineer Company- 4 platoons, again a brigade level asset
Support BN- Medical company which assigns out a medic to each company along with running BN & BDE aide stations, the Distribution company looks like the current catchphrase for BDE supply/ordnance, and a maintenance company
For BTU purposes, substitute regiment where I say brigade above and realize BTU has a brigade composed of regiments which would be the equivalent of divisions in US Army afaik. The 3 Maneuver BNs are the 'line' units, everything else falls under the Rgt/BDE's authority and get broken up to support the combat tasks assigned to BN. If you are assigned to support a BN you are called an attachment/detachment depending on verbiage.
Though I will be honest, I was part of a artillery brigade which was assigned to a division, so mirror this and go up 1 level . . . and the doctrinal shift to Brigade Combat Teams happened when my unit was changing equipment and alternating deployments to Iraq so it was never as clear as the Division model that was used post-WWII so someone might offer better insight since we were never tasked to a maneuver BDE.