Seems a bit starter related. Sort of like banging on it might work sometimes. It gets the starter in a different point of its revolution and easier to spin. Jumping it direct from the battery gives a slightly higher voltage since it is not travelling through longer wires and an old relay, and gets it to spin. Then at some point you get unlucky again and won’t start with the key. Eventually all options don’t work because the starter is too far gone. That was my situation. And outside temp affected it.
Also turning the key a bunch of times sometimes gets it working, but then you begin to wear out the relay and maybe the key barrel.