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If this is going to be a disk that's permanently installed, you would typically just enable the boot menu recovery option by using the "Windows Boot Menu" option in Rescue Media Builder. But if you're trying to create it on a disk that will not always be attached, then you should not be performing Steps 3 and 4. Your Step 3 command is telling Windows to put a copy of Windows Boot Manager onto that partition and create a BCD entry in that instance that will boot into your regular Windows environment, which is definitely not what you want for Rescue Media. And Step 4 is unnecessary. First, Diskpart has a command that will create a properly configured EFI partition anyway ("create partition efi"), but a Rescue Media partition is not an EFI partition, nor should it be designated as such. The purpose of an EFI partition is to be set up using a firmware-supported file system (e.g. FAT32) and store the bootloader files that the system firmware will read and that will then allow a full OS to be booted from a different partition that will typically use a file system that is NOT firmware-supported, such as ext4 (Linux) or NTFS, which is optional to support under the UEFI spec and thus not widely supported. That's not what you're trying to do here.
All you need to do is create a FAT32 partition and copy the Rescue Media files to its root, but then you would boot from it when desired by invoking your system-level one-time boot menu. Technically you could register the \EFI\Boot\Bootx64.efi bootloader file on that partition as a regular boot path into your system's UEFI firmware, but the much more common use case is to use one-time boot menus just as you would for a Rescue Media flash drive that you'd attached.
Note however that if your GPT hard disk is attached via USB, I've encountered some systems will not boot from USB "fixed disk class" devices like hard drives and SSDs, and will instead only boot from USB "removable storage class" devices like flash drives. If you have such a system and that isn't resolvable with a firmware update, then you're out of luck. If you have a properly populated FAT32 partition and have that disk connected at boot and you still don't see a new option in your one-time boot menu at that point, then that may be your issue.
I've also encountered some systems that will only boot from Partition 1 of storage devices initialized as GPT, even though they will happily boot from later partitions if that same device is re-initialized as MBR.