How do I recover lost app data from an older iCloud backup version?

I was trying to restore my phone from the most recent iCloud backup. Before starting the restoration, I checked the backup details and saw that one of the apps I needed had over 3GB of data. I assumed everything would be fine.

However, after resetting and restoring my phone (which showed that the restoration was complete), none of the app’s data was recovered—only around 300MB of the base app itself. When I went back to the backup section, I found that my original backup had already been deleted and replaced with a new one.

Does this mean that I’ve permanently lost all of that data?

While searching for solutions, I saw some people mention that it might be possible to retrieve older backup versions (even though the official documentation states only the most recent one is kept). I also used some third-party tools to scan, and they showed that there was a backup from April. That data is extremely important to me—is there any chance of recovering it?

[Re-Titled by Moderator]

Original Title: Lost Backup Data