Do you have access to an iCloud backup for your old iPad Pro? If so, you could try erasing your new iPad and restoring it from the iCloud backup. That would resurrect your 1Password on the new iPad. I don't believe they are under any obligation to host old iOS installers on the App Store.
BTW, I purchased 1Password several years ago before the days of subscription, and it still gets updated regularly, now at version 7.9.3. I have upgraded my phones and iPads several times, each time from an iCloud backup, and 1Password has come along for the ride. So I'm not sure I buy the security argument.
I also have 1Password 7 for the Mac (perpetual license) which also gets updated from time to time. Thankfully, this is a Universal build, so it works on Apple Silicon or Intel. Last week, I got an Apple Silicon MacBook Pro, and the installer ran ok. The version 7 installer is still available on the downloads area
https://1password.com/downloads/mac/ but I made sure I had a copy of the installer and license file on my machine, just in case. When starting up for the 1st time on my new MacBook, it asked if I had an iCloud vault (which I did), and it announced that I am licensed, so I didn't need to use the license file again.