muscle soreness can have a variety of causes. As you outline it I would assert the muscle soreness is a result of working a muscle that is not used to being worked, and perhaps working it quite rigorously. Whether it is your walk or your practice I simply could not know as you’ve not said anything about the nature, type, frequency, or duration of your practice.
Sore muscles (by the definition we’re giving them here) are in a repair state. The time for that repair varies, it is not fixed, and can take anywhere from 48 to 72 hours. This repair depends on how throughly exhausted the muscle is during the work and, of course, how one eats, sleeps, and lives.
I would not place additional demand on repairing muscles. That is to say if your legs are sore I would not do a full standing pose sequence. When the muscles are in repair you have less chance to find and maintain proper alignment.
However doing poses that do not place great demand on the sore muscles is okay, presuming you are not fatigued. When you come down from inversions as a result of fatigue please do not go back up.
Relative to sirsasana you mention another important point; comfort in the pose. Unfortunately “comfort” is often undefined and subjective. If you are UNcomfortable in the pose then of course its benefits would be reduced. By how much I cannot say, nor would I if I knew. Many students work uncomfortably in asana so you’d be fitting right in with most western practitioners:-) If you cannot find joy in sirsasana due to the quadriceps then find another pose.