cant see MacBook air hard drive in sierra

Refer to How to reinstall macOS - Apple Support, with these instructions:

• On an Intel-based Mac, you can use Shift-Option-Command-R during startup to be offered the macOS that came with your Mac, or the closest version still available.

If your Mac shipped with Sierra, that is the version it should install.

High Sierra ought to suffice though. I am not aware of anything that works with Sierra that would not work with High Sierra.

You appear to be using a third party NVMe SSD. When using a third party NVMe SSD, you can only use macOS 10.13+. If you want to use macOS 10.12 Sierra (or macOS 10.11), then you will need to reinstall the original Apple SSD.

Back up all data before proceeding. Do not omit that step.

Select the topmost device, and erase it. If you are asked to choose a format, be sure to use Mac OS Extended, and not APFS. This is important because earlier macOS versions will not recognize APFS, and you may find yourself in a situation in which no internal devices will appear.

Then, shut down the Mac, boot macOS Recovery and follow the instructions in my previous reply:

• On an Intel-based Mac, you can use Shift-Option-Command-R during startup to be offered the macOS that came with your Mac, or the closest version still available.

Please be advised you will be doing something that I am unable to personally verify at the moment, so proceed accordingly.

Don't boot from the flash drive. Remove it and set it aside for now. Boot Recovery mode again and select Disk Utility. Then, from its View menu, choose "All Devices". Take a picture of that screen.

Neither of those images appear to indicate the presence of a Sierra installer, but set that concern aside for now because it is not yet clear to me whether that flash drive is usable. If Apple's instructions are correct, you should be able to erase the internal drive and reinstall Sierra, but Disk Utility needs to see that internal drive first. You should not require either flash drive.

Apparently that Mac shipped with El Capitan, the OS X version just prior to Sierra.

There needs to be a "Show All Devices" option under a View menu, which does not appear to exist on its version of Recovery. Boot from your Monterey flash drive again and see if it appears. The key is to format that internal drive using the GUID Partition Map and Mac OS Extended.

Once Disk Utility is able to see that device, you should be able to quit Disk Utility, install El Capitan from Recovery, boot that system, and subsequently upgrade it to Sierra.

Any Mac capable or running Monterey is too new to run Sierra.

Identify your MacBook Air model - Apple Support

Did you also choose "Untitled" and erase it, using Mac OS Extended as its format?