It sounds hormonal, but I think you’re also reinforcing his fear by chasing and cornering him. Rabbits only squeak when they are deathly afraid, so he is genuinely afraid.
Lots of young bunnies enjoy being carried and cuddled, but as they mature, they tend to become far less tolerant of this. Both of my male bunnies were the cutest, cuddliest little things when they were babies. They would literally curl up and sleep on my lap, but now they absolutely wouldn’t tolerate it. They still like me, and they still come over for attention when they want it, but it’s on their terms, and they wouldn’t just chill out on my lap for hours anymore. So I think you need to accept that he’s probably not going to be as cuddly and chilled as he was when he was a baby, but you can still have a great relationship with him.
So, while it is worth getting him neutered, as it does sound like some of his behaviour is hormonal, I think you also need to change some habits, and adapt your expectations of him.
Firstly, stop taking him in and out the cage yourself – he should be able to enter and exit the cage himself to stop these situations where he’s being chased and hiding in a corner. This might mean you need to adapt his cage, but your relationship will not improve while you’re chasing him twice a day. It’s essential that that stops. When I want my bunnies to go back into their pen, I just put some veggies in, and they know that it’s dinner time and happily go back in by themselves. Sometimes I have to herd them in, but I’m not chasing them, and there’s a treat at the end.
Secondly, stop trying to play with him and fuss him. The best way to interact with him is to sit on the floor, and let him come to you when he’s ready. Don’t immediately stroke him or fuss him. Let him learn that you’re not always trying to pick him up or chase him. Give him treats/pellets/veg and slowly build up trust with him.