Workaround for getting older Keynote and Numbers apps that aren't in my previous purchases?

OK, I need to check my thinking on something...

I have a late 2015 iMac running Catalina which I'm about to update to Monterey (the latest OS my machine can run). This means I will need to update some of my Apple apps though the App Store, such as iMovie, Pages etc.

That's all fine, but two apps I need - Keynote and Numbers - came with my machine, and I've never downloaded them from the App Store before. This means they don't show up in my previous purchases, which in turn means Apple won't let me download older Monterey-compatible versions. When I try, it just says I need MacOS 14, which my Mac cannot run.

So how do I get round Apple's unhelpfulness?

Well my daughter has a MacBook which is running, I think, Sonoma. So it occurs to me that if we set up a new user on her Macbook, make that user me, with my associated AppleID (AppleIDs are linked to users, not devices, right? Or have I got that wrong?) then I can download Keynote and Numbers onto her machine under my AppleID which will put them into my App Store previous purchases, which then means when I go back to my 2015 iMac, I can download those apps again, this time to Monterey, and the App Store will automatically download the latest version compatible with the Monterey OS?

So I guess my question is, will that work?

Thoughts welcome.

Thanks in advance.