macOS Sierra doesn't appear in my Purchased list within the Mac App Store

Contrary to past OS releases where the N-1 installer is removed soon after version N launches, Apple has an article with links to the store and detailed requirements for getting and installing macOS Sierra (even after High Sierra is out).

• https://support.apple.com/en-us/HT208202 - How to download macOS Sierra
• macOS Sierra Installer on the Mac App Store

I would use the help article HT20802 to check for an updated link if the Mac App Store one fails you. As soon as you get Sierra installed, I would make a bootable USB drive for your personal rescue kit - especially if macOS Recovery isn't available for your hardware or typical network situation.

• How do I make a bootable USB flash drive a Mac?

The download of macOS Sierra is not linked to an Apple ID. In fact, users can download it without having to sign into the Mac App Store.

Another recent change made by Apple is the inclusion of an additional macOS Recovery option. Instead of two, we now have three options:

• commandR to reinstall the latest macOS that was installed on your Mac, without upgrading to a later version
• optioncommandR to upgrade to the latest macOS that is compatible with your Mac
• shiftoptioncommandR to reinstall the macOS that came with your Mac, or the version closest to it that is still available¹

¹ That third option is a new option only available since 27 March 2017 and requires macOS Sierra 10.12.4.

The result of these changes is that in future, if you need to install a compatible version of macOS that is earlier than the one that is still available, you will need to have a copy of the installer.

In summary, if you wish to have a version of macOS available for possible future installation, it is recommended that you download and store the relevant installer so that it is available to you. You don’t need to install it to do this, you can download it via the Mac App Store and then quit the installer when it launches. You can then make a copy of it for future use.

[Update as at 3 October 2017]

This edit provides an update on how users can access a macOS Sierra installer for Macs that already have macOS High Sierra installed.

As I previously recommended, if you wish to have a version of macOS Sierra available for possible future installation, users needed to download and store the relevant installer so that it was available to them.

After discussion with Apple today (3 October 2017), the following is how things will work if you happen to want to install macOS Sierra on a Mac that already has macOS High Sierra installed (assuming the Mac in question supports a macOS Sierra installation):

• If your Mac originally shipped with macOS Sierra, then the easiest option is to use the shiftoptioncommandR recovery option to reinstall macOS Sierra
• If your Mac did not originally ship with macOS Sierra, then the only official options are:
  1. use a copy of the macOS Sierra installer that you've previously downloaded and saved (if you have one), or
  2. take it into an Apple Store where they can install macOS Sierra for you (but how long this would be an option was questionable).

IMPORTANT - If your Mac originally shipped with El Capitan or earlier and also supports a macOS Sierra installation, you cannot use the shiftoptioncommandR recovery option to reinstall the original macOS in the hope you can then upgrade to macOS Sierra. Instead, doing this will only result in the Mac App Store offering macOS High Sierra as the next upgrade option.

In relation to option 1 above, if you can obtain a copy of the macOS Sierra installer through other means (such as from a friend), then this will also work. Obviously, downloading the macOS Sierra installer from dubious sources is not recommended and is at your own risk.

[Update as at 18 October 2017]

Please refer to bmike's answer. Apple has just published a new help article that provides a way for users to install macOS Sierra.

IMPORTANT:

If you're downgrading from 10.13 to 10.12 on a drive formatted as APFS, then DO NOT downgrade using macOS Sierra (10.12 Installer) disk utility to Erase your disk. Instead you HAVE TO use the Online Recovery tool (or High Sierra (10.13) Disk Utility) to Erase your disk from APFS back to HFS+, then restart and use your macOS Sierra installer from USB.

If you use Sierra to Erase disk, you'll get stuck in a Reboot Loop which is what happened to me.