It's the plain meaning of the verse from Tehillim 147:19 which says:
מַגִּ֣יד דְּבָרָ֣יו לְיַעֲקֹ֑ב חֻקָּ֥יו וּ֝מִשְׁפָּטָ֗יו לְיִשְׂרָאֵֽל׃
That all the laws and judgements in Torah which G-d commanded to the Jewish people are also observed by G-d. This follows one of the long-standing teachings the Lubavitcher Rebbe like is found for example in Torat Menachem Hitvadiyut, vol. 3 from the year 5711, pg. 12 notes 26-27
And like the Rebbe cites from Yerushalmi Rosh HaShanah, chapter 1, Halacha 3 which says:
בנוהג שבעולם מלך בשר ודם גוזר גזירה. רצה מקיימה רצו אחרים מקיימים אותה אבל הקב"ה אינו כן אלא גוזר גזירה ומקיימה תחילה מאי טעמא ושמרו את משמרתי אני ה' אני הוא ששימרתי מצותיה של תורה תחילה.
This is the same sentiment that is also expressed by Rabbi Avin Bar Rav Adda in relation to tefillin as found in Berachot 6a, which says:
Rabbi Avin bar Rav Adda said that Rabbi Yitzḥak said: From where is it derived that the Holy One, Blessed be He, wears phylacteries? As it is stated: “The Lord has sworn by His right hand, and by the arm of His strength”
And so the answer to your question should be found in the laws of Shabbat.
Rambam in Mishnah Torah, Hilchot Shabbat 24:7 which says:
[A court] may not punish on Shabbat. Even though the punishment is a positive commandment, it does not override [forbidden types of work on] Shabbat. How is this? If one surely become liable for lashes or the death penalty, we neither give him lashes nor kill him on Shabbat; as it is stated (Exodus 35:3), "You may not kindle fire in all of your inhabitations on the Shabbat day"—this is a prohibition to the court that, on Shabbat, they not burn someone who became liable for burning. And the same is true with the other punishments.
However this raises the same question you raise. Does this prohibition only apply to the execution of the judgement or the process of judgement itself?
But if one considers the first halacha in that same chapter, the prohibition would seem to extend even to the judgement itself which would be like discussing with your business associates, meaning those Judges sitting with you on the Jewish court, what business to take up the next day.
In other words, actual deliberation of the case and judgement, while leaving the execution of the judgement until after Shabbat, is also prohibited on Shabbat.
Mishneh Torah, Hilchot Shabbat 24:1
Some acts are forbidden on the Sabbath even though they neither resemble nor lead to prohibited work. Why then were they forbidden? Because it is written: "If you refrain from following your business on the Sabbath, on my holy day… If you honor it, not following your wonted ways, not pursuing your business, nor speaking of it" (Isaiah 58:13). Hence, one is forbidden to go anywhere on the Sabbath in connection with his business, or even to talk about it. Thus one must not discuss with his partner what to sell on the next day, or what to buy, or how to build a certain house, or what merchandise to take to such-and-such a place. All this, and the like, is forbidden, for it is written "nor speaking of it." That is to say, speaking of business on the Sabbath is forbidden; thinking of it, however, is permitted.
And it is worth noting that the last comment from Rambam in this halacha appears to be an insight into the judgement of Rosh Hashanah, for example, when it falls out on Shabbat. Rambam emphasizes that thinking about business matters is not prohibited on Shabbat.
And so, in context G-d could think about how a judgement would be deliberated in the Heavenly court and how it might resolve.
But this last concept needs to be understood in the context of the teaching of Eliyahu HaNavi that is found in the P'tach Eliyahu recited at Mincha of erev Shabbat. G-d's thoughts are not like our thoughts. From our perspective, G-d's thoughts are like a completed action, even though by G-d it is thought.
And this idea relates also to the concept of G-d judging someone unfavorably on Rosh HaShanah. And yet through our actions through the remaining cycle of Tishrei, that judgement can be overturned.