(I haven't yet tried to set my own avatar, so not emperically tested to the max, but...)
It is possible that the forum is taking the (valid) "https://..." and, because the 2016-vintage PHP (I presume) at the backend doesn't truly understand that it is prepending "http://" onto the otherwise proper URI. The profile field is prefilled as that (so it could also be Magmacube not deleting that when they pasted in). The (presumably) php might just be silly like that. If you save the utterly correct setting and revisit it and it's wrong, then you just can't https it, as it is.
The [img]-tag as submitted by the user goes through a subtly different system between poster and reader. That's a regexp (or something very similar) that takes a presumed-correct URI and shoves it into a true HTML <img src="..." /> format (or similar) to serve to all the readers' browsers and works for any "Content-Type: image/jpeg" (or equivalent) returned data purely based on the browser but the forum backend has no server-side checks to make sure that it's not a container-page. The avatar-accepting code[1] will likely be just as happy to let the user make this error. (The alternative is that the server does a pre-emptive web-spidering, which seems like a recipe for maliciously getting forums to suffer/take part in DDOS efforts with very little user effort.)
[1] Maybe an experiment needs to be done to see if a browser that accepts an <img src="whatever.svg" /> (without an onerror= fallback setting) can be used to display an avatar set to be a suitable whatever.svg, but a number of browsers will not. For this reason, I suspect there may be a basic sanity-check for either a restricted subset of extensions (with or without appended GET options) such as ".jpg, .jpeg, .gif", or apparently extensionless references (might cover an ".../image.jpg?width-400" example), but it'd depend a lot on the thoughts of the original backend-scripter on this matter. (Including if they give it as an option for the site maintainer to reconfigure.) And various implied standards have changed over the last handful of years in this area of markup usage and browser parsing/rendering, such that I'm not even sure I'm up to speed myself.