Can God really be in sorrow?

Peace be upon you, Rabbi, and fasting is beneficial.
There is a point where I am able to connect with the destruction of the Temple, the point where G-d was closer and a person could atone for his sins, and I also connect with the desire for redemption because I hope that the troubles will end and the Jewish truth will come to light.
But I’ve heard it several times already: They say that the greatest and highest reason to desire redemption and mourn the destruction is that the Shekhinah is in sorrow, meaning that G-d has no home and it hurts that we are in exile.
I fail to understand this because God truly does not have emotions like humans and the Rambam writes that even when he writes titles, it is only a guide.
But this does not mean that God is truly angry and has wrath. If this is truly the case, how can we connect with sorrow that is not truly sorrow and is just a show so that we know what to do???
It’s like my friend making an angry face at me and I know he’s not really angry with me and he just wants something from me, do I care about his angry face??? Of course not!!!
 
???
Thank you very much.