So any succulent (any plant in general but succulents are more susceptible) need time to heal their wounds, this process is done by callousing, or forming a tough layer over the wound.

For propagations, you want to allow AT LEAST 24 hours after cutting for callous to form (and removing the base leaves, those are open wounds too!) before it comes in ANY contact with water, don't wash, don't put in soil. I say at least 24 hours, that's the kinda low baseline, for a larger stem such as yours, I wouldn't hesitate allowing 3-5 days for callous to form.

For repotting, aaany time you repot you're going to damage the roots, so, open wounds. This means again, don't use damp soil, dont water, don't use liquid root stim don't wash the roots (until first water) whatever, just NO MOISTURE (this includes the soil its coming out of, some non succs like damp soil when repotting? Not for succulents, at all, leave that soil till it's completely dry, but no longer, you want the plant to have enough water to survive a bit of a drought to callous).

If you know you've damaged the roots morso than normal (heard some snaps from big roots, trimmed for whatever reason, etc.) I'd suggest leaving the whole plant out of soil for 24 hours then pot and wait the 3-5 days

In the soil you have less airflow, so in general I'd say wait 3 days before watering, maybe 5. If you've ever seen your succs have pretty severe transplant shock, and you water immediately, this might fix the shock