The logout redirection sends you back to the /administrator URL. That's hardcoded into Joomla. I'd love to change that, but I haven't been able to come up with a way the core devs would accept to change it in the core.
Something you can do is enable the "allow re-entry" setting, which opens a short window where you can immediately log back in without a key. When enabled, you can specify how many seconds re-entry is allowed with no key. When enabled, logging out will display the login form (no 404, no strike) from which you can navigate away.
I'll have another look at that problem. I'm always learning new things and coming up with new and interesting ways to do things I'm not supposed to do Maybe a loophole exists that I didn't see previously.
I just started testing in the new Joomla 4.0.0 beta 1 - so I'll be in the code for the next few days. I'll have a poke around and see what rules I can break.