I know this is definitely possible.
In 2019 I had access to a new Mac using the current macOS of the time. I "purchased" Pages, Numbers, Garageband. I had never had them previously. I then went to my old Mac running Mavericks. When I went to the App Store and looked under my purchases, I saw Pages, Numbers, etc. in my purchase history. I tried to redownload it but got the error message you got. However, it also said there was an older version I could download and did I want it? Yes, I did, and it was installed on my 8 year old computer. Incidentally, they then appeared as a possible downloads on all my old iOS devices too.
Four days ago I was given a computer with Big Sur. I went to the Mac App Store and found Pages etc. in my purchase history saying I had purchased it in 2019. I tried downloading it and got the same messages about the current version needing a newer macOS but did I want a Big Sur version? Again, I successfully got an older version on my computer.
The trick may be to do as léonie suggests and once you have successfully purchased it on a supported system, to then look at your purchase history on the old system.