Cloak All I know is the existing ISO won't install on my new HP laptop ...
Two things you might do:
(1) Swap drives.
If you still have your old laptop, you might try taking out the drive from your new laptop, taking out the drive from your old laptop, installing the drive from your new laptop into your old laptop, installing on the old laptop, updating fully after installation, and then returning the drive to your new laptop. At that point, your new laptop will boot into the current version of Solus. At lot of work, I know, but I've used that method and it works.
(2) Disable discrete video card.
If you have an Intel CPU with an onboard GPU, you might try disabling the discrete GPU (probably Nvidia) and installing using the Intel onboard GPU, updating fully after installation, and then enabling your Nvidia CPU.
In either case, I would wait another week until the kernel has been updated to 6.0. Kernel 6.0 will have the latest possible drivers for your hardware.