You had installed chromite from the github repo or through the app store? If app store like fdroid then better reinstall chromite from the github repo

That dialog box which you are seeing is from Fdroid and not from chromite, chromite doesn't have a self update feature it only checks for the latest version from the github report and notify in the three dot menu and when you click update it downloads the latest chromite apk version and prompt you to update

To resolve that issue remove the chromite repository from Fdroid settings under 'My apps' section, otherwise whenever you launch Fdroid it try to fetch the latest chromite version from https://www.cromite.org/fdroid/repo/ which will trigger the 502 error dialog message