I'm not sure there's an answer for this, as it seems like it's a new bug introduced with the new webstore, caused by trying to download non user-specific links for some files.
Basically, my base chrome profile is my base, personal seaders@ google profile. My work profile, however is [email protected]. We're developing a chrome extension which is currently in a closed beta, the development version will always be in closed beta, and never be publicly available.
If I access that extension with via my work profile https://chromewebstore.google.com/u/1/detail/super-streaming/extensionidyadayada I can go there without an issue, and everything looks to be working right. However, if I click "Add to Chrome", I get a spinny, and then an error message "Download Error: Access Denied". If I go there with my personal profile, /u/0 I correctly can't access the page at all.
As an added point, if I also access the dev dashboard, via my work profile, https://chrome.google.com/u/1/webstore/devconsole/bigfatid/extensionidyadayada/edit/package again, I can access it perfectly fine. If I try to download the published main.crx file there, the link is https://chrome.google.com/webstore/download/extensionidyadayada/package/main/crx/3 I get a 403 and no access. If I edit that link to a user-specific link, https://chrome.google.com/webstore/download/extensionidyadayada/package/main/crx/3?authuser=1 I can download fine. If I try to access the dev console with my default account, /u/0, I correctly can't access the page at all.
This bug has only been introduced since the new webstore, https://chromewebstore.google.com, when it was the old https://chrome.google.com/webstore there was no issue.
I can also verify the issue by adding my personal / base user to the google group that controls the closed beta access. I don't want to do that, nor should I have to.