I didn't realise there was more than one photo. My brain may be playing tricks on me but I only saw the one with the cardboard lol.
If a spring breaks it's more likely to break at the bottom on the last coil or two. Where the bottom of the spring sits (I said cup but probably should have said seat?). It will often be broken around the back of the spring so it is difficult to notice on first glance.
If it's not broken I guess you could have mismatched springs, or just old and tired springs.
Suppose you could have a strut/shock problem too but I'd be surprised if that would have you generating a clunking noise just by rocking the roof of your car by hand (I think you wrote that. Apologies if not.)
Anyway, I'm not a mechanic so I'll step aside and perhaps someone with more knowledge can step in and advise you
