The "View" option located just above the left pane of Disk Utility is only available with macOS 10.13+. You can see the "View" option in the screenshots provided by @Grant.
Just because you booted into Recovery Mode using Command + R or Internet Recovery Mode using Command + Option + R does not mean you are booted into a macOS 10.13+ online installer. Look to see which OS is listed on the main menu of the recovery mode page to see which specific version of macOS is listed to be installed.
As long as you actually installed macOS 10.13+ on this laptop at some point in the past, then the laptop has the necessary system firmware to work with an NVMe SSD. The only remaining issue regarding the system firmware update is if you want to install macOS 12.x Monterey. To install macOS 12.x Monterey for the first time requires an original Apple OEM SSD installed internally since the Monterey installer will refuse to run if a third party SSD is installed internall if the system firmware needs to be updated. So this means if you want to install Monterey to the new SSD, you must first install Monterey while the original Apple OEM SSD is installed internally in this laptop. You can install Monterey to either the internal or external drive to update the system firmware as long as the original Apple OEM SSD is installed internally. After Monterey has been successfully installed one time, any later reinstall of Monterey can be done with the third party NVMe SSD installed internally.
I only mentioned the Monterey system firmware update issue because if you can boot to the online Monterey installer in Internet Recovery Mode (Command + Option + R), then you won't be able to complete the installation of Monterey while the third party NVMe SSD installed because the Monterey installer insists on updating the system firmware, but will only update the system firmware when the original Apple OEM SSD is installed internally.
You should have no problems installing macOS 10.13, 10.14, 10.15, or 11.x to the third party NVMe SSD assuming the SSD is working & compatible with your Mac (and any SSD adapter is compatible if using an M.2 SSD).