Simple question: does Hawkeye (2021) start after the end of Spider-man: No Way Home, or are the series’ near Christmas events when Rogers: The Musical is playing coincident in time?
As per this site's analysis, likely Spider-Man: No Way Home precedes Hawkeye (2021)
Spider-Man: No Way Home picks up directly after the events of Far From Home, which means it also takes place in 2024, though heading into the start-of-school/fall season.
Hawkeye is set at the end of 2024, during the Christmas season. It sees Clint Barton dealing with the consequences of his tenure as Ronin, the vigilante alter-ego he took on during the Blip.
It seems likely that No Way Home ends before the end of Hawkeye, as the Rockefeller Center appears to be fine in the final scene.