Safari lost half my extensions and passwords after a system crash
As you may have noticed from my question, I was very determined to find a solution and finally I found one. If you have a Time Machine setup then you're lucky. All you need to do is to restore those 4 folders (remember to select all the contents from the backup) to the time before the crash.

~/Library/Safari/Extensions/

~/Library/Keychains

/Library/Keychains

/System/Library/Keychains

(Probably not all are needed, but this worked for me)

Restart and open safari to check that everything is on place. Re-enable Keychain if it was disabled (mine was enabled, but turned to disabled in this process). Enjoy.