Is it possible to dig out an old project through this account?

I worked on a project in 2015 and left it half complete. I want to pick it up, but my computer from back then no longer works and I can’t find the files in any of my online drives.
Can I somehow use the fact I used this account to dig up the files?

No, the Epic Games Launcher/Unreal Engine service does not have cloud storage for projects, any time you make a project that content is only stored on your computer. That’s why it’s good to use an online backup system like Perforce/Git