Those all sound like software issues from Sony on their headset, rather than limitations of Bluetooth. I have a pair of BOSS that is connected to both my laptop and phone at the same time, and the switch between them is seemless.
Listen to music on phone. Pause, go to laptop. Put on a video on YouTube. And it instantly switches to my laptop for sound.
Be on a call on discord from my phone while I'm out. Get home, enter the call from laptop, and boom. Automatically switched from phone to laptop and I don't have to change a single setting.
Sorry you have a bad experience with SONY. But I can assure you. It's not a Bluetooth problem. It's a SONY problem.