Edit 1: I searched in your install log and found the installer actually tried to change your partition table into MBR but failed so it’s not the cause. The answer below "="s may be misleading. You may try to change the partition table yourself and try again. The Jan topic mentioned using fdisk (or gdisk) to convert your drive into MBR. I found multiple advices suggesting defferent ways, hard to tell which of them are correct. Will edit again when I confirm. You can also try to google yourself during that.
Edit 2: Found a Arch Wiki using sgdisk. Could be helpful:
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This time I couldn’t find any useful information by myself so I asked AI for you. So the thing is your laptop seems to be booting in Legacy mode instead of UEFI while your hard drive is in GPT format instead of MBR (which is required if you are booting in Legacy mode). I searched google and found a topic back in Jan with similar issue:
So it seems to be a bug of cachyos installer as it formats your drive into GPT whichever boot mode your pc is in. You may follow this guy’s suggestion and download an older installer of CachyOS. Don’t worry about older software stuff as Arch Linux which Cachy bases on is a rolling update OS so simply run a pacman update command and your system will be up to date. For your installer USB if you don’t mind I strongly suggest you to use ventoy
since it enables you to store and boot from any one of multiple .iso files instead of only one, which is helpful since you are having 2 installers involved in your situation.
AI also suggests you to check BIOS of your laptop to see if there are any options to switch your boot type to UEFI. But it says your laptop may be too old and probably only supports Legacy so using an older installer seems to be the quickest way to solve your problem.