I would like to have a multi boot system with Win10, an Ubuntu or Debian based distro and Garuda Linux dr460nized (it is pronounced dragonized, just in case anybody is wondering).
All of them are 64bit on a UEFI computer.

Win10 and MX Linux ( = Debian based) are installed already and working fine.

Now I'd like to add Garuda Linux (see here, 1st picture), which is an Arch based distro with a customized KDE desktop.

But I'm not sure about the Grub installation, because I don't want to destroy anything that's already present on my computer, of course.

Where exactly does Garuda install Grub on a UEFI system, with an already existing EFI partition?

If Garuda creates its own folder, let's say /garuda or /arch or whatever it is called, I guess, it should be possible to boot into Garuda, delete the /garuda or /arch folder from the EFI partition and reinstall Grub by adding the following code to the Grub installation command, bacause, up to now, MX19.2 is the efi folder used by Grub:
Or I might use a SuperGrub stick, boot into MX Linux, delete the /MX19.2 folder from the EFI partition, reinstall Grub, creating a neutral folder (like this one for example: /linboot) by adding this code to the Grub install command:

MX Linux will be the default distro by then.

Then I boot into Garuda and reinstall Grub by adding the same bootloader-id code. Now Garuda is the default distro.

What are the chances for this to work like that? What do you think?

This is assuming you selected manual parittioning.
If you want Garuda bootloader to be in control, at the partitioning stage highlight the efi partition and edit, set mount point to /boot/efi, do not select format. When the grub bootloader is installed during installaion, it should become the default bootloader. If not you will have to go into the firmware/bios and to make Garuda bootloader the default.

If you pefer to not install Garuda bootloader and continue to use the mint bootloader, do nothing as far as the efi partition and ignore the message that your system may not start. After installation, boot into mint run to produce a boot entry for Garuda.

I just managed to install Garuda in a Virtualbox with EFI enabled. That's how I found out that the folder with the efi files (probably inside, I guess) is called "Garuda" with a capital "G". Now, I'd like to access that folder to find out what's actually inside and what the size of those files is.
Unfortunately, I can't find any information about how to open that folder with admin privileges.
On my Mint with Caja, I only have to right-click the wanted folder, click "Open as administrator" and enter the password.

In Garuda, I need to access that folder with Dolphin, to see the size of the files inside.

Finally, I want to know, if I have to resize my efi partition which is currently 100 MB. That size used to be enough for the efi files required for Win 10, Ubuntu, and even more.

EDIT: I just found the size of the efi partition, using the KDE partition manager. According to that, the size of the efi partition is 360 MB and only 560 KB of it is used.
Now, I wonder, what do I need an efi partition of that size for, if my physically existing efi partition is 100 MB, which should be way more than what is required for even a multi boot system?

If you want something for a reference, my efi partition is using 110MB. in the EFI It has 4 directories with grub bootloaders, one with an elilo bootloader, refind bootloader, a windows bootloader, a hp directory, On the partition is an EFI directory, boot directory with a grub bootloader, two configuration files, and two other small system directories.
In the EFI directory has 4 directories with grub bootloaders, one with an elilo bootloader, refind bootloader directory, a windows bootloader directory, a hp directory,and a boot directory with another bootloader in it.

If the space after the efi partition is already in use by linux or windows it would be best to leave alone. You will spend more time fixing then what it would be worth for what little space you will gain by downsizing the efi partition. If only going to multiboot one or two distros 100MB should be more than enough. If you do a lot of installing and uninstalling different distros with a 100MB you will need to delete the leftover bootloader directory that is usually left behind on the efi partition when a distro is removed to keep the efi partition from filling up.

Thank you for this information.
I just noticed the efi partition of the wanted computer is 260 MB already, so, no resizing seems to be necessary.

Have you ever tried Garuda on a multi boot system? It creates a folder called "Garuda" in the EFI partition. But the question is, does it add that folder to the already existing ones or does it replace the existing ones?
If the latter is true, this would be real bad, because all other systems wouldn't boot anymore and on a HP computer the HP folder with the "HP PC Hardware Diagnostics" tools would also become lost.

What's worrying me most, is that dual or multi boot is not officially supported by Garuda, therefore I'm afraid of destroying something of the existing installations.

Another question:
On an Arch, which Garuda is based on, do you know how to access the efi folder which is in /boot/efi?
So far, I didn't find a way in Dolphin to get in that folder, because there is no context option like "Open as root" or so.

Did a multiboot install with Garuda in a vm, Garuda added to what was already on the efi partition.
you will have to use sudo with the ls command in a terminal.