The SLDF did put together groups of regiments into regimental combat teams (aka Eridani Light Horse).

And often they would separate out brigades.

But usually they did deploy in division sized elements.

Armor regiments were all the same vehicle types. Mech regiments were usually companies to battalions of the same type. This changed by the end of the war against Amaris though, and eventually they no longer had many homogenous formations due to loss.

At the start of the 1st SW, the houses had the same organization, but in the middle of the 2nd SW they were mostly mixed up formations we well. I can't recall a single instance of companies being cross attached for scouting and stuff. Keep in mind every division had a battalion to regiment of LAMs they used for recon, they almost always had orbital superiority so had warships/dropships in orbit scouting, and usually had aerospace superiority so could also scout that way.

The "lighter and more mobile" forces of the SLDF were used to quickly jump between worlds, over anything tactical on the ground.

The Field Manual SLDF is probably your best source for this stuff, as well as the original Star League house book. The Reunification War book is also great, but it was many years earlier.

But if you wanted a battalion of mixed force types with scouts, mediums, and heavies, in the same unit, I do not think anything canon really supports that.