TL;DR RSPH did not claim 63% of Instagram users are 'miserable'. The Economist claimed an "activity-tracking app" collected data that showed 63% of Instagram users are "sad with the amount of time they spend on each app." It is incorrect to say 63% of Instagram users are "miserable".
Both links in the question cite a Royal Society for Public Health (RSPH) report. I have read the entire RSPH report (link here). While nominally 32 pages, it is covered with images and graphics and actually ~16 pages of text. Based on my reading, the report does not make the claim that Instagram users are "miserable," "less satisfied," "unhappy," etc.
In light of this, I searched up additional sites that made these claims. The earliest such site is The Economist making the claim on May 18, 2018 (emphasis added).
And data from Moment, an activity-tracking app, show that it is possible for light social-media consumers to be content. Each week it asks its 1m users whether they are happy or sad with the amount of time they have spent on various platforms. Nearly 63% of Instagram users report being miserable, a higher share than for any other social network. They spend an average of nearly an hour per day on the app. The 37% who are happy spend on average just over half as long.
This makes it clear that the claim isn't reported by RSPH. Instead, it is reported by an "activity-tracking app," Moment. The Economist included the below infographic, which makes the source (Moment, and not RSPH) much clearer. We can see that "Happy users" spend ~35 minutes on Instagram, "Sad users" ~60 minutes, and "All users" ~50 minutes. Note that the infographic states "% of users who are happy with the amount of time they spend on each app" and not whether they are happy or sad in regards to life. (emphasis mine) 37% of users are happy with the amount of time they spend on Instagram. This may not mean 63% are not. And not being happy with the amount of time you spend on Instagram does not mean you are miserable. This clarifies the meaning of the source and shows the two sources in the question are misinterpreting the original data.
The other two sites mentioned in the question both misattribute the statistic to RSPH. This may be because RSPH is more credible than a random app. They also misinterpret the original data.
I wanted to confirm this data directly from Moment, so I looked at their site. Near the bottom of the page, there are logos and links to ~90 articles from various news sites that mention Moment. Unfortunately, The Economist is not mentioned on this page. Moment also has a blog. The data also was not on the blog. I was able to verify the "1m user" number used by The Economist.
It’s amazing how far we’ve come. Over 7 million people have downloaded Moment all over the world...That all adds up to a whopping 49 years of time we’re giving people back every single day!
As the author of The Economist article is referred to as "THE DATA TEAM" instead of an actual author, I contacted both The Economist and Moment to verify my interpretation and learn more about the original source. For Moment, I emailed both known email addresses. The same page writes "We will read each email and usually get back to you within a week. Sometimes, it might take us two weeks to respond to each individual email." Moment did not respond to any of my emails and it will soon be a month.
The Economist replied to my emails without providing new relevant information. The latest reply read: "Any requests for additional information or sources of articles are usually shared at our discretion." I assume this means they are not willing to confirm the data and its original source.
I do not expect any new information from The Economist or Moment.
Are 63% of Instagram users 'miserable'?
No, the 63% are simply unhappy with the amount of time they spend on Instagram. They do not necessarily feel "miserable," so the use of the word "miserable" is most likely an exaggeration.
