It's indeed very confusing.
I even realized that, while both the Conversion Tracking and Remarketing Tracking tags are different per se, the Global Site tag they provide under Tag Setup is exactly the same.
So basically, installing the Global Site tag manually shoots up both the Conversion and Remarketing tag (as I confirmed using the Tag Assistant extension). But for some reason, the Google App sales channel - after installing the Global Site tag automatically - shoots up only the Conversion tracking tag.
Since I was confused, I asked their support about this and here's what they said:
"As much as I would love to dive in and help you out further we aren't able to support integrations with Tag Manager or remarketing campaigns. There are third party app solutions available on the app store that you may want to consider as an alternative: C.E for Google Ads & Shopping or Retargeting for Google Ads."
I still can't understand why the Google app can't just activate both tracking tags.
Either way, I did realize the issue of the duplicate Global site tag seems to appear only on the Google Tag Assistant Legacy extension for Chrome. Using https://tagassistant.google.com/, as Emmanuel recommended, doesn't show any duplicate tag alerts.
Also, I guess the duplicate tag is more like a warning than an actual error, so it seems more like a minor annoyance and a technical error that could breaking something. Since I've installed it manually, following instructions and the parameters are being correctly pulled, I might as well just like the duplicate Global tags.