Great! Now we know to test the differences in Incognito mode.
Alternatively, you can add another user profile in Chrome (also in the other browers?) which has its own set of cookies, extensions, site settings, saved form fields, website permission, history, and maybe other details. A profile saves those settings separately from the first profile, whereas an Incognito window discards them when closed. A separate profile is very likely to fix the problem, and it's easy to open when needed, so that could be a fine solution.
Both an Incognito window and a new profile should start with default settings, leaving out whatever settings are getting in way.
One way to proceed is to start with a regular window and try turning off all the extensions. (Click Chrome's puzzle piece icon or the 3-dot menu, then open Manage Extensions. I don't remember the details for other browsers.) Then try logging in.
If that doesn't do it, keep the extensions off, open a tesla.com tab, click the padlock icon to the left of the URL, and click Site Settings. That'll open a tab that controls all the brower permissions for tesla.com. You can click Reset Permissions or look down the list for non-default settings and change those. Again try logging in.
If that doesn't work, the problem must be one of the other differences with Incognito mode, possibly in addition to extensions and/or permissions.
You already ruled out the cookie hypothesis, although they can come back quickly so you might have to delete them again, at least the ones listed in the padlock icon's Cookies section. Actually, in addition to Cookies in Use, that section has Cookies Blocked. Any cookie blocks there could easily be the problem. It's fine to clear out the Blocked section, then test again.
