Easy mode fix for you if it is pooling in that corner.

You can buy a "gutter spigot" (that only works on flat bottomed gutter, like your ogee or square styles.) - Or that's what i've always called them, You simply hole saw a 54mm hole in the flat of your gutter, pop the thing through, screw it down and attach a down pipe.

Link to english site selling this. - https://www.trulypvc.com/roofing/rainwater/unions-outlets/hunter-uni-fit-r400-gutter-outlet

I'm sure you can get them in every country. not sure if it will be called the same thing.

As someone else said, clean out the gutters and reseal the joins first and foremost, but this won't solve the pooling issue.