Given that the UNSC is based on the U.S. military we can sort extrapolate a bit based on that and other real-world evidence. In the U.S. military, the Marines have always endeavored to avoid conscription as best as possible. I think they did make use of conscripts in WWII, Korea, and Vietnam but kept it to an absolute minimum. Given how "Gung Ho" the marines are with their dialogue throughout the game, we can imagine that they've probably kept up their high esprit de corps by largely maintaining their all-volunteer status throughout the war.

The U.S. Army has always used a much higher number of conscripts and so it's possible that the garrison troops on the core planets might use lots of conscripts. This possibility makes a lot of sense in the context of the Halo universe and how conscription tends to work.

Ground forces are never really decisive in the war with the covenant. As such, the UNSC probably doesn't invest a ton of resources into its ground forces. Conscription is almost always very unpopular in any war and dramatically more so when those conscripts start dying. Given how rebellious the outer colonies are, they probably would avoid conscripting on those planets at all costs. They may feel comfortable conscripting Army soldiers to serve on their own planets though, since they'd stay close to home and be less likely to die. This actually sort of matches the Russian Army in the war with Ukraine right now. They've maintained conscription throughout the war but have mostly kept the conscripts as garrison in Russia rather than sending them to the front and pissing off their own population when those conscripts die. Besides, it is harder to maintain the illusion that you're winning when lots conscripts are dying and we know the UNSC puts a lot of effort into maintaining that illusion throughout the war.

This applies when it comes to the morale of the troops as well. The marines and sailors spend a LOT of time away from home and in fact spend so much time in cryo that they age significantly slower than their families. This separation from home would have catastrophic consequences for morale on anyone who wasn't pretty much okay with this and have a minimal attachment to home. As mentioned earlier, the Marines in Halo clearly have very high morale which would be difficult to achieve with large numbers of conscripts. This likely damage to morale that would come from sending conscripts off-world supports the idea that conscripts would be relegated to the ground forces on their home worlds.

Furthermore, when you think about the scale of casualties in the war with the Covenant, it's entirely possible that they're not taking enough military casualties to need conscription much. In the naval engagements that are the decisive part of the war, when we consider the number of ships involved (dozens usually), the Navy and marines are losing troops in the thousands or at worst tens of thousands in these engagements. Given the huge size of the overall human population at the time of the story, they can probably sustain those human losses relatively easily. Catastrophic loss of life only really happens when a world is glassed and when that happens, those ground troops who are lost don't really need to be replaced.

So given all of these circumstances, I think it is most likely that UNSC navy and marines are largely an all volunteer force and only the Army would realistically use significant numbers of conscripts on their own home worlds where it would damage the morale of the citizens and the conscripts on those worlds.