I usually split it into two steps, not because it’s mandatory, but because it gives you one last chance to catch issues before the cover goes on.
After shocking and balancing, I like to let the pool circulate for at least a full evening or overnight. That does two things. First, it lets everything actually mix and react instead of trapping fresh chemistry under the cover. Second, it gives you a final look at the water the next day. If it’s cloudy, smells off, or the chlorine got chewed up faster than expected, you can fix it while the pool is still accessible.
Another small benefit is off-gassing. Strong chlorine right before covering can get trapped and sit against the cover underside all winter. Letting it circulate with the pool open for a bit helps that burn off so you’re not sealing in harsh conditions.
If the weather is stable, waiting a day is usually worth it. The only time I cover immediately is if a storm is coming or temps are dropping fast. Otherwise, that overnight buffer has saved me from a couple of “wish I caught that first” openings in spring.