Replace Startup disk on MacPro Mid 2012

It is a common debugging technique to NOT copy MacOS, but instead install it from fundamental sources. MacOS never modifies itself on purpose, so this gives you a clean copy. ALL customization is done through preference files.

Time machine is moving away from copying MacOS itself as part of your backups, and newer Macs will not install MacOS from the backup, if present.

At first run, you have the opportunity to specify a new userid. DON'T do that. Instead, tell setup assistant your files are located on (Pick one): {your old drive, on your backup drive}

This old screenshot will give yo an idea of the choices that will be offered:

Move your content to a new Mac - Apple Support

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If you can get the new drive installed BEFORE you remove the old drive, it will be FAR simpler.

Otherwise, you need s source of Utility software or a bootable USB-stick installer.

Internet Recovery is NOT available in your model’s ROM, so you will need to explore this list of other possibilities.

When your computer was released, the way you launched the required Utilities (including Disk Utility and Installer) was to use the ones on the Release software DVD. if you have a model-specific version for your model (unlikely) or a Full Retail 10.6 DVD, you use its Utilities, boot and install that version, then use Software update to get to 10.6.8 with all updates, which is the version that can reach out to the Mac App store and download and install a later version. 10.11 El Capitan is a recommended waypoint, even if you expect to install a later version, because it has an improved Mac App Store that makes getting later versions much easier.

The next source of Utilities is the Recovery Partition on the boot drive. If your drive spins up, even if not MacOS bootable, it may still have a usable recovery partition. To get there, try invoking recovery with Command-R or hold Alt/Option at startup and see if the recovery partition shows as a potentially bootable drive.

Recovery Partitions up through 10.12 Sierra can be found with the Startup Manager (Alt/Option boot). At 10.13, if an SSD boot drive is used, the format is transitioned to APFS. The Recovery partition is present, but it is inside the APFS volume structures, and the Startup Manager on an older Mac can not find it.

The next source of Utilities to consider is any MacOS 10.6 or later versions on any additional drives or clones you may (or may not) have lying about, even if they are from another Mac. You can use those Utilities to ERASE a new drive, and start the installer to place MacOS on the new drive.

The next source to consider is a Time Machine backup drive. Versions from 10.7.3 or later are said to contain a Recovery Partition that could be used to ERASE a new drive and run Installer to place MacOS on a new drive.

IF you have a different Mac, you can use it to download MacOS install image, then interrupt the process and create a BOOTABLE USB-stick Installer/Utilities stick. BOOTABLE is key, because the way you will install from this USB-Stick is to BOOT the USB-stick, and use its Utilities to ERASE your drive and start the Installer. here is the article on bootable USB-Stick Utilities/Installer:

What you need to create a bootable installer

• A USB flash drive or other secondary volume formatted as Mac OS Extended, with at least 14GB of available storage

• A downloaded installer for macOS Big Sur, Catalina, Mojave, High Sierra, or El Capitan.

from:

How to create a bootable installer for macOS - Apple Support

How to create a bootable installer for macOS - Apple Support

NB>> if you name your incoming USB stick exactly MyVolume, you can copy and paste the very long Terminal command from the article directly into the Terminal window, without having to change anything.

Mac Pro silver tower does not care which drive is in which bay -- they are equivalent priority.

If you have an open bay, just install the new drive (replacing the standard sled with the SSD on a sled).

Launch disk Utility and make certain "show all devices" is available.

Elect the new drive by its immutable device-manufacturer-assigned Device-name.

ERASE. (for High Sierra and later, choose Apple File System APFS)

Then download and run the MacOS installer, and select the newly-erased drive as the place to install.