The ~/Library/Keychains location is within your home directory and is user specific to your account on the Mac.
The /LibraryKeychains the one with system.keychain is for all users on the Mac and is not where your passwords are normally stored. Other things like certificates are stored there.
The ~/Library folder is hidden in macOS Finder. If you click the Go dropdown menu in Finder and hold the Option key the hidden Library will appear on the dropdown menu. Click on it and then you will see the Keychains folder and within is your login.keychain.
Then you can open Time Machine while inside the Keychain folder to roll back time. Copy the login.keychain-db to another location like Documents or Desktop. Then open Keychain Access and add it so you can examine the contents. You'll see two login keychains when you add the second one.
Alternatively, if it's not a Time Machine backup you can navigate to /Users/<username>/Library/Keychains on the backup disk and copy the file and add it to Keychain Access to examine it.
You will have to know the password if it's different than your current Mac password to unlock the encrypted login keychain file. There is no way to reset the password, you have to know what it is to unlock it.