@SimplyBeautifulArt I am not sure what you mean by blog through chat and whether by our own blogs you mean Math.SE blog or blogs of individual users.
But since math.SE blog had very low activity in the time when it was officially supported, I have my doubts whether this could change now that the only option is to create it on an external site, outside of the SE network.
That's supposed to be an example what you meant by the phrase blogs through chat, right?
Well, to me it seems that nothing has changed.
Nobody prevents you from posting messages in chat and bookmarking conversations.
It is very likely not ideal format for somethings which is intended as a blog, but it was possible before blogoverflow was cancelled and it is still possible now.
@SimplyBeautifulArt Maybe this would be worth reporting as a bug. Still I will ping mixedmath to see what he thinks - he seems to be most experienced with blogoverflow around here.