The problem in the UK is that experienced nurses only make £35k ($47k) a year, and then they wonder why there’s a shortage of nurses and we all get locked up for months so “save our NHS”.
The care home staff shortage is inexorable because it’s a shitty job that doesn’t require much skill (maybe empathy) and so it’s not a promising career. You need a lot of them but can’t just pay a lot more because people wouldn’t be able to afford care for their relatives. The answer there is to reduce the need for labor through automation, AI and robotics.