Perhaps the reduced quantity of oil ran hotter, thus thinning out and increasing noise?

so I can understand the cold-start rattle. What I don't understand is why adding oil should help.

So it did it with cold oil, nothing to do with thinning when hot.

I can think of several possible reasons:

1) Oil pump worn, so it struggled to build up initial pressure, but immersion in a greater depth of oil would help it to prime.

2) Incorrect oil filter lacking a non-return valve, so took longer to re-prime.

3) Is the timing chain pressure lubricated or does the crankshaft sprocket sit in oil gravity-fed from the sump?

Oil that has been circulating in the engine has been picking up comtaminants and long-chain molecules in oil tend to get broken up in use - new oil will have intact long-chain thickeners and this may quieten things down for a while.