Normally you would need to have had iMovie on your computer at one time in order to download or update it. So you might not be able to get iMovie 10 unless you purchase it from a third party website that is not authorized by Apple. There are some risks of malware from doing that. In any event, to get the current iMovie verion you would need to upgrade Catalina to Montery or Ventura.
For the last few years iMovie has come pre-installed on Macs. Even if iMovie had been lost or deleted, it still could be updated under the Apple I.D. used when it was first purchased. One could use the regular update procedure from the app store, or if that didn't work, you could sign in at the app store with your Apple I.D. and update iMovie from your Account page. As you have found, the problem with acquiring a second hand computer is that any iMovie app that may have been on it at one time would have been acquired with someone else's Apple I.D. Thus it could not be updated unless you had the previous owner's I.D.
To cover the bases, check the Applications folder of your inherited older Mac to see if iMovie 10 is there. If it's there, the you do have it. You could try to update it as described above. If you don't see iMovie use the hidden purchases procedure described below.
Since you do have or have had other Mac computers it is likely that iMovie 10 was installed on them at the time of purchase. Check your Applications folder. If iMovie is not listed as an app, Sign into the app store with your current I.D, and/or the one used when you purchased the computers. Check your Account page to see if iMovie 10 is listed there. If it's not listed, check to see if it may be a hidden app by clicking on the "View Information" tab at the top right of the Accounts page.
When you click on View Information another screen will pop up that will enable you to reveal any hidden purchases.
In the above screen click on Manage and see if you can find iMovie there, and reveal it in the Purchases page. Try updating or downloading it from there.
If you can download iMovie on one of your other computers, perhaps you can drag the app onto your inherited computer.
-- Rich