I tried copying Debian 10 by unmounting then "cp" to usb as this guide at 4.3.1 states https://www.debian.org/releases/jess...-copy-flexible

But I get this error when I try to boot to it; how do I solve it

PS: why does linux copy iso as an extraction when volume/usb is unmounted. And what does "unmounted" in the world of linux mean?

If I understand you properly, you are attempting to copy an install to a usb device before even looking up what mount means?
Perhaps some reading is in order. The terms mount and unmount suggest themselves, but also the details of the command "mount" and "umount" on unix (including Linux) style systems. Examining the drives (and mounts) on a running Linux system is also suggested.

It says that it should be copied while my USB is in an unmounted state

I even saw the contents after mounting and they where in.

What are you trying to achieve here? Install Debian? Because then you are going about it the wrong way; what you linked states:
The document you linked is also for jessie, now EOL.

https://www.debian.org/releases/stable/installmanual

I was trying to have the installer purely on USB

By the way, why does the .iso file extract when the USB is unmounted but copies when it is mounted?

The download the iso and write it to the USB. You are talking about a thumbdrive, no?

OK. Linux makes a distinction between a disk as a physical device and the filesystem on the disk.Just plugging a memory stick into a usb port does not make its contents available. For that, you have to "mount" it on an empty directory. This directory (the mount point) then becomes a synonym for the root directory of the disk, so that all the subdirectories and files become accessible to you. You must then unmount the drive before removing it to ensure that it doesn't get corrupted.

On the other hand, if you want to create a bootable memory stick, you need to do a raw physical copy of the disk image onto the device itself. So that device must not be mounted at the time.

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what is in your syslinux.cfg file? You need to only have in it what the guide says for it to work: , otherwise you need to copy vesamenu.c32, libcom32.c32, libutil.c32, and copy isolinux.bin and rename to syslinux.bin to the usb. Even then it may not work if the version of isolinux/syslinux on the iso image is different from the version on the system your doing this from, for different versions of syslinux/isolinux don't play together well.

If what you want is to create a USB device with one or more ISO images from which you can boot and install, look into E2B (Easy 2 Boot). It is the best tool I use for that purpose, with it I can carry a couple of USB keys and have a choice of booting and installing dozens of different distributions from which I select at boot time.

Depending upon your resources and experience, you might also look into MultiBootUSB, SARDU, and YUMI.