Thank you for your question. It’s great you’re asking about the meaning of these supplications. Not many people recite them regularly and even less reflect upon their meaning.
This is one of many affirmations that the Prophet (peace and blessings upon him) taught us to make in the morning and evening and at other significant times. The translation you quoted is quite literal, which makes it require a bit of explanation. I prefer to translate it as follows:
“Evening has come upon us, and to Allah belongs all sovereignty.”
When we translate it like this, it becomes clearer that the person saying these words is affirming a timeless reality – that the kingdom or sovereignty belongs to Allah alone and no one else. That is, of course, the case at all times, but the person confirms that reality at this particular time. In other words, the affirmation relates to the state of the person making the affirmation and the time they are making it. As for Allah and His kingdom, it makes no difference whether it is morning or evening.
(Ibn Allan, al-Futuhat al-Rabbaniyyah)
I hope this answer is helpful.
May Allah bless you and allow us all to witness these realities in the morning and the evening and at all times.