Is it possible apps that didn’t actually exist on the phone to be stored in library?

How likely is it that you find apps you don’t recognize in the Library section of Google Play?

Unlikely. The Library shows all apps associated with that account, and for apps to be linked, they had to have been 'installed' to a linked device (even if you just wanted to get a free game, you'd have to install it on a device or click the install button on the Play store website to remote install to a device). You might not remember the app or maybe it was bundled with an old phone, but it was, at some point, at least attempted to install onto one of your devices (even if the installation was canceled before the full download was completed, the app would then be linked tonysiur account)

If you have your Play Account on another person's device, that person's downloads also show up.