It’s a problem of the installer. With cachyos-desktop-linux-260124.iso in the summary of the last install step it always says “create GPT Partition table on /dev/sd…” instead of MBR. With cachyos-desktop-linux-251129.iso it creates a MBR partition table.
So just try this iso: https://cdn77.cachyos.org/ISO/desktop/251129/cachyos-desktop-linux-251129.iso
Before you start the installer please create a MBR with fdisk first. Edit: You can skip this step. Not necessary.
But I can’t help with the encrypted swap!