Okay I've just checked with my 3-letter-named account and it is exactly the same as shown in Gothness' screenshots, getting a "The change you wanted was rejected" error on my own profile as well as on everyone else's. It is safe to say every account that doesn't show a web profile to others ("We're sorry, but something went wrong" error) will see "The change you wanted was rejected" error on their own and on every other resident's profile.

This means the way to reproduce this is the following:

1: Create a new test account whose name is 3 letters or shorter or not much longer (I've seen some long names that don't have a web profile but all with 3 letters are showing this error so it might be easier)

2: See if the web profile of the test account shows "We're sorry, but something went wrong" when you are not logged in with that account.

3: If it shows the error, log in with that account and see if it shows "The change you wanted was rejected" instead of anything else on its own and on everyone else's profile.

If you don't get the "something went wrong" error on the test account, make a new one and repeat until you get one that has this error - some new accounts have a web profile and some get this error permanently.

That's a weird one! I have seen that error once while trying to figure out what was going on with the web profiles. I've noticed that in late 2023 or early 2024 new accounts, especially if they have a short name, started to show this issue where they don't have a web profile and instead "We're sorry, but something went wrong" shows there. While messing with checking profiles of recently created accounts, I saw this one in your post, too.

Around the same time this started to happen, I also noticed that there must have been a change in the names that are allowed by the system. Were 3-letter names always allowed? Then how come Cat and Dog were only taken about a year ago, not way back in 2010? These accounts also don't have a web profile.

I think the source of this can be found around the changes that were made in the account sign up and allowed names at that time. (I will edit and specify time when I'm inworld since I can't check the web profiles that don't exist)

Edit: September 2024 is when the Cat and Dog accounts were made that don't have a web feed, and they are both 3-letter names and clearly names that someone would have taken way sooner if they had been available. So my suspicion is there were some changes made to the sign up system in 2024 (not necessarily September, it might have taken some time until people realized they could take these names) and those changes managed to break the web profiles of new accounts. However, not all new accounts have this issue, and as visible in the OP's screenshot, Robo's feed shows the rejected error too, who is not a new account at all.

For reference you can see below that Gothness' profile shows the typical "something went wrong" error for me, and Robo's shows "nothing shared at the moment".