Only the current version of macOS is available from the Mac App Store, and no full installer is available from Apple's downloads site.
If you are currently on macOS 10.15.7, then you have solved the 32-bit to 64-bit application requirement and your 2017 Air can upgrade to Big Sur (11.7.2), or Monterey (12.6.2). You would still need to confirm that your third-party vendors support their applications on the later operating systems, and that includes your printer/scanner vendors who may not…
If you are satisfied with paragraph two, then backup to Time Machine one last time, get the later operating system from How to download macOS - Apple Support using the Safari browser. Do not use that same Time Machine drive for your first (or any) backup of the upgraded operating system.
If on the other hand, you are still on macOS Mojave or earlier then you need to pay even closer attention to Big Sur or Monterey compatible applications from third-party vendors as these must now be 64-bit applications and Adobe CS?, Apple's iWork '09, and Office 2011 for Mac are all incompatible with Big Sur and beyond. I would recommend the free Go64 application to determine what is 32-bit in the current operating system (Mojave or earlier).