To be precise, I'm trying to understand this in regards to the Dark Shadows, who are a special forces unit in the covert operations branch of SAFE. What I have on them is a snippet from Handbook: House Marik, as detailed below;
"Intended for matters that require force rather than finesse, the Dark Shadows are SAFE’s independent BattleMech troops, the only such governmental unit outside the FWLM (from which it draws its soldiers). The Shadows’ operations and details are hidden from public view, but their existence is an open secret, albeit one colored by myth and misdirection."
And that's it. So, what kind of missions would these guys perform? The only thing I can think of at the moment is risky false-flag ops and perhaps deep raids, but what else might they do?
The ISF had (has?) a similar unit that got a brief mention in the NAIS 4th SW atlas. Check out the battle of Crossing which served as the climax of the private war between Kurita and the Dragoons. Dropping behind enemy lines right onto their HQ to sow panic and confusion into the mercenaries? Check. Into terrain so rugged you'll lose half your mechs just pulling the maneuver off? Check!
Besides the "we need troops so loyal they'll accept the suicidal mission" trope:
Internal Security: Dealing with nobles and other actors that are getting too powerful and too uppity in their #resist campaign against House Marik/the FWL. They'll often have their own private armies, which can necessitate an army to neutralize them. FWLM units can be of questionable loyalty, especially provincial regiments. If you want to go to the extreme of going after Duke Uppitybritches, you want troops that won't surprise you by having sympathies with him.
Cadre duty: Training FWLM forces as OPFOR. General proficiency training, or even posing as LCAF/CCAF forces in a wargame for FWLM forces.
Deep strike raids: The line FWLM forces handle most raids, sure. But maybe right at this moment the best company of mechwarriors available for a long duration raid without outside support or backup is special forces.
Headhunter missions: Special forces rarely operate solo- they're usually a small force attached to the larger campaigning army that take on special missions. A lance or company of Dark Shadows could very plausibly be on detatched duty with a line FWLM regiment, taking on specialty missions like seeking and destroying enemy C2 units.
Pirate hunting: I imagine that a LOT of special forces work in the BTU involves pirate hunting. Why? Because pirates get by on intel. They know where and when to raid, and when to GTFO before the hammer comes down. not to get all real world on this thread, but very much the same dynamic with real world drug cartels in Mexico. The police and army are often thoroughly penetrated by the cartels, so who usually gets the "go" order for an offensive strike/bust? The Mexican Marines. I envision the same dynamic in the BTU.. regular House army has such a hard time striking pirates because the pirates always get world from their contacts in the House Armies in time to get out of dodge. OTOH if you send a small, tight force like special forces, your OPSEC is presumably better and more likely to actually catch the pirates by surprise.
Also: the BTU has always been ruled by the rule of cool moreso than practical real world military concerns. There's lots of movies (and lately) tv shows focusing on commandos, lots of inspiration there to be scaled up to mech-size.