The EFI partition doesn't actually have much critical information. It's a regular FAT32 partition that contains one small program (the Windows boot manager) and its configuration file. It doesn't actually deal with things that the firmware can already do by itself (such as detecting DVDs); its job is just to tell the firmware how to boot one or other OS specifically.
You're correct that everything is installed as part of Install.wim (or .esd) image. However, it doesn't come in the form of a pre-made "EFI partition" – it comes in the form of regular files under C:\Windows.
The entire Install.wim image is unpacked to your OS partition, producing such directories as C:\Windows and C:\ProgramData.
Files that consist the Windows boot manager are copied from C:\Windows\Boot\EFI into the desired place within the EFI System Partition (usually under \EFI\Microsoft).
The "BCD" configuration file is generated, telling the Windows boot manager about where to find the main OS partition.
A boot menu entry is added to your firmware's NVRAM, telling it which file (Bootmgfw.efi) is the Windows boot manager.
You can do all of this yourself; step 1 can be done using dism
and steps 2–4 can be done using the bcdboot
command, both of which come with Windows. (In fact, that's basically all there is to a Windows installation.)
Other operating systems work similarly. (For example, to install systemd-boot on Linux, you just copy the program file /usr/lib/systemd/boot/efi/systemd-bootx64.efi into the EFI System Partition and create a text file that points at whichever Linux kernel you want to boot...)
To be precise, the EFI information must be present to "help" the motherboard perform that first "recovery boot-from-DVD",
Yes, but during boot from DVD, you're only using the EFI files that are on the DVD itself.
and must be present to then be transferred onto the first partition of the new HDD (for subsequent "help" in normal boots).
No, the EFI files used to boot the DVD are completely independent from those used to boot the final OS. They are not copied; instead the files from the OS install image are used.
What happens when I do a "recovery boot-from-DVD" when the HDD has an already-functioning OS - If I choose to install to an empty partition, keeping the old OS for dual-boot, is all of that EFI data on the DVD ignored (since the HDD already has an EFI data partition)?
The bootloader is OS-specific, so each OS almost always needs to install its own copy.
What happens when I install over (i.e., overwrite) the old OS - Does the EFI partition stay or get replaced?
Usually it stays; the installer will err towards keeping possibly useless boot entries instead of removing possibly needed boot entries.