Help to upgrade OS on 2011 MacBook Air that has been wiped with OS X 10.6.8 reinstalled

How I got back to High Sierra on my wiped 2011 MacBook Air:

1. I wiped my 2011 MacBook Air (built late 2010), but found that there was no way to reinstall macOS High Sierra.
2. I used the supplied USB "Reinstall Drive Mac OS X v 10.6 iLife 11", then updated to get to OS X 10.6.8 Snow Leopard.
3. Using https://support.apple.com/en-au/HT211683 "How to get old versions of macOS", I tried OS X Yosemite 10.10, which it said could upgrade Snow Leopard. After downloading the installer I could not find it after restarting. But turning off then on (instead of restart) put the Yosemite installer in the Applications folder. I installed it, then upgraded to OS X 10.10.5 Yosemite.
4. Using https://support.apple.com/en-au/HT211683 I then tried OS X El Capitan 10.11, because it said that could update Yosemite. But that was a dead end. El Capitan failed to install and dumped back to the start, meaning I had to reinstall the supplied USB and climb back to Snow Leopard (Step 2) and then reinstall Yosemite back to OS X 10.10.5 Yosemite (Step 3).
5. Using https://support.apple.com/en-au/HT211683 I then tried macOS High Sierra 10.13, which it said can upgrade Yosemite (avoiding Sierra - in case it repeated the dead end of El Capitan). That worked, I have reached macOS10.13.6 High Sierra.

Thanks. Somehow I managed to download Yosemite, then found it (it was hiding in my applications folder ready to install) and it worked. So I have installed all the updates and patches for Yosemite and now I am in the process of backing everything up on TimeMachine. Then I will attempt to download and install El Capitan, and at least if that fails I will have my TimeMachine backup as far as Yosemite.

Yes, since you said that about dates I have seen that some people do that to get ahead, reset the date to something early like 2010. In my case so far it has not turned out to be necessary.

Before I managed to install Yosemite I was contemplating a long route of installing Lion, then Mountain Lion, etc. But strangely, Apple charges for downloads of Lion and Mountain Lion. I can't fathom that, especially when I was getting desperate and had no idea whether any download of any operating system beyond Snow Leopard would install properly.

Also, at one stage when I phoned Apple Support they wanted me to download High Sierra on another Mac, move it to a USB and use that. Apparently that used to be the solution. So I tried to do that, but the Mac was running Catalina, and that operating system (and now Big Sur) assumes any download of an older OS is trying to stupidly install that older OS as an update, so will not download it, not even to put on a USB. Since then I have seen that very method suggested, ie find another Mac, download High Sierra, move it to a USB and use that to start up the old Mac that needs High Sierra. Once upon a time that method must have worked, but it does not now.

All I can say for myself so far is that a 2011 MacBook Air can download and install up to Snow Leopard, which can then download and install Yosemite, and from there with any luck I might be able to download and install El Capitan, and keep going until I get to High Sierra.