You can try these steps in case of issues with webpages:

You can reload webpage(s) and bypass the cache to refresh possibly outdated or corrupted files.

• hold down the Shift key and left-click the Reload button
• press "Ctrl + F5" or press "Ctrl + Shift + R" (Windows,Linux)
• press "Command + Shift + R" (Mac)

Clear the Cache and remove the Cookies for websites that cause problems via the "3-bar" Firefox menu button (Settings), click the padlock icon (Clear cookies and site data) for the domain in the selected tab.

"Remove the Cookies" for websites that cause problems:

• Settings -> Privacy & Security
  Cookies and Site Data: "Manage Data"

"Clear the Cache":

• Settings -> Privacy & Security
  Cookies and Site Data -> Clear Data -> [X] Cached Web Content -> Clear

• https://support.mozilla.org/en-US/kb/clear-cookies-and-site-data-firefox
• https://support.mozilla.org/en-US/kb/how-clear-firefox-cache

Start Firefox in Troubleshoot Mode to check if one of the extensions ("3-bar" menu button or Tools -> Add-ons -> Extensions) or if hardware acceleration or if userChrome.css/userContent.css is causing the problem.

• switch to the Default System theme: "3-bar" menu button or Tools -> Add-ons -> Themes
• do NOT click the "Refresh Firefox" button on the Troubleshoot Mode start window

• https://support.mozilla.org/en-US/kb/diagnose-firefox-issues-using-troubleshoot-mode
• https://support.mozilla.org/en-US/kb/troubleshoot-extensions-themes-to-fix-problems

You can check for issues with Enhanced Tracking Protection. Firefox shows a purple shield instead of a gray shield at the left end of the location/address bar in case Enhanced Tracking Protection is blocking content.

• click the shield icon for more detail and possibly disable the protection

You can check the Web Console for relevant-looking messages like blocked content.

• https://support.mozilla.org/en-US/kb/enhanced-tracking-protection-firefox-desktop
• https://support.mozilla.org/en-US/kb/total-cookie-protection-and-website-breakage-faq
• https://support.mozilla.org/en-US/kb/trackers-and-scripts-firefox-blocks-enhanced-track

Unfortunately, my problem is still not resolved. I tried everything you suggested, as well as clearing all browsing data (cache, cookies, history), disabling all extensions, turning off Enhanced Tracking Protection, and disabling two-factor authentication for my Mozilla account, but I am still getting the same page (see screen shot in my original post) when attempting to sign in to the add-ons page. Might there be any other measures to take?

Are you trying to sign in to the Developer Hub? I am able to sign in without issue but I have never used authentication.

Thanks for checking, Terry. No, I'm not trying to sign in to the "Developer Hub". Rather, I am clicking on the "Log in" link at https://addons.mozilla.org/en-US/firefox/.

My problem is now resolved. The "Connected Services" settings of my Mozilla account indicated that I was signed in to Add-ons. This was strange because the Add-ons site said I was logged out, and my attempts to login were unsuccessful, leading to the internal service error page (see original post). Well, I clicked "Sign out" from the Connected Services page, navigated to the Mozilla Add-ons page, and was finally able to sign in again. I guess it was a problem on Mozilla's back end.