Usually using the website on PC, tablet and phone, so I didn't know, where you were coming from with the missing 'log out'.
When I click my user icon on the website, it's always there as the last option on the left.
I was sure, that there was an edit option for posts, though perhaps it's time-restricted? I have amended posts in the past, due to suffering from text prediction and fat finger syndrome myself.

Though I tried a couple of my older posts yesterday there was no edit option on the website on either tablet or phone.
(there was an edit option just now, when I reopened this post and I was able to add this)