Controller software updates suck. As far as I know there isn't a way to trigger them yourself. Once you say "wait 24 hours" you must wait 24 hours.Settings > Accessories > Controllers > Wireless Controller Device software
Xbox updates controllers without needing to plug them in but it's pretty slow.
It was added in an update a few months after launch.
PS5 updates are weird.
There's System Software Update, and then there's System Feature Update, with no real description of what the latter is for.