What you could try: make a copy of the file you are seeing with your tool and move it somewhere else to secure it.
Launch Illustrator. When you launch it and it finds something in the Receovery folder, it will try to recover it. It will show a popup and ask if it should do that. You have to say yes. Otherwise it will delete the recovery file. When it fails to recover it, then that's that.
File recovery is not a backup solution. And should not be used as such. It can spare you the hassle of recreating the last 20 minutes. But don't ever try and rely on it for more than that timespan.
You said the computer was without power. If it runs out of power while saving that is the absolute worst moment for power outage. And that includes the file recovery.
Save early. Save often. Save different versions. And then you can use file recovery.
That said: maybe @Anshul_Saini can help you with the copy of the recovery data you have. You can hope for a miracle of some sort, but the chances are slight.
Sorry to hear about that. You may share the recovery file with me, and I will check if it is recoverable or not. Generally, when recovery data is recovered from any third-party recovery app, it overrides the recovery data, which leads to data corruption.