Seamless metal. It's leaking along the length of the gutter, not just
the junction. If I had to guess I say it is seeping through the
puncture whole of those spikes.

Is it standard 3 X 5" seamless gutter ? The water should never get near the
top..but should drain faster. First check the drains where the downpipes
are connected to the gutter for crud/leaves etc. If they re clean, then
what size are your downpipes..I recently saw a Home DIY/Fixit show where
they used crappy 2" x 2" downpipe...No good.