The main meaning is to administrate. This is the job of a clerk or a civil servant.
Ich verwalte meine Zeit.
means, that you have a calendar and for everything you will do in the future is a entry in your calendar. Zeit verwalten doesn't mean that you are making plans for your future. It just means that you avoid colliding appointments and that you track them, so that you always know when you have to be where.
But verwalten can not be used for time only, but for any resources. There is a profession, and the German name for it is Verwalter. A Verwalter is a caretaker, trustee, custodian, curator or a manciple. Their job is to know what is going on and to keep things running and to keep them intact. If someone else needs to use some of the resources, the Verwalter makes notes and assigns the resources.
The job of a Verwalter is not to have new ideas or to plan future activities. So, sometimes Verwalter is used to name people who never have new ideas and who don't show any creativity.
In 2019 there was a severe government crisis in Austria. On the parliament's behest the federal president displaced the whole government, and for the few month that were needed to prepare new elections, he installed a new government that was not built from voted politicians, but from so called "experts" which he had selected. Since this intermediate government was not elected by the people, they decided not to navigate the country into any direction, but just to keep it running. So, the motto of this intermediate government was »verwalten statt gestalten« (administering instead of creating).
This means to govern, to regulate, to steer, to control, to navigate.
Somebody who does this is making plans and is leading things in the direction they want. On a ship you have the Kapitän (captain) who is responsible for the whole ship and a Steuermann (cox, steersman, pilot) who leads the ship into the desired direction. What this cox does is steuern, and this word also is used in its figurative meaning when you control a company as CEO or even a country as a politician.
But you can not steuern time. This would mean that you have influence on how fast or slow time flows. This is not possible. You only have influence about what to do in certain sections of time. But this is verwalten, not steuern.
The German verb managen means to manage and maybe is the best choice in your sentence:
Ich habe meine Zeiteinteilung geplant, weil ich die Zeit managen muss.
The only trade-off is, that it is a foreign word, but German language has a very long history of adopting words from other languages, and managen already is so common, that it really is ok to use it, even if there is the German word verwalten that also fits quite well here.
the noun "timing"
In your original question (before I edited it) you used the noun Zeitliche as translation of timing. This is terribly wrong. The noun Zeitliche is rare and is used only in this fixed phrase: »das Zeitliche segnen« (literal: "to bless the temporal") which means "to die", "to pass away". So, I replaced it in your question with a German words that fits well, but still is not the best choice.
dict.leo.org displays 22 different translation just for the naked noun timing and 145 more translations for combinations of timing with other words. The German words that fits best into your sentence are Zeiteinteilung or just Zeit (which even isn't in the list of dict.leo)
- Ich habe meine Zeiteinteilung geplant, weil ich die Zeit verwalten muss.
- Ich habe meine Zeit geplant, weil ich die Zeit verwalten muss.
Variation 1 is very close to the english sentence, but Zeiteinteilung is a cumbersome word that sounds a little bit bureaucratic.
I would prefer variation 2 if there wasn't the relative clause, because in the relative clause you repeat the word Zeit which is bad style
OK: Ich habe meine Zeit geplant.
ugly word repetition: Ich habe meine Zeit geplant, weil ich die Zeit verwalten muss.
But in the relative clause you have no good alternative for Zeit, so neither 1 nor 2 are good choices.
But German has the super power of adopting foreign words, and so this is a very good alternative:
- Ich habe mein Timing geplant, weil ich die Zeit verwalten muss.
The noun Timing is a very well know foreign word, and here it is the best choice.
Note, that "das Timing" in a neuter noun, so the possessive pronoun also has to be neuter ("mein Timing") while both, "die Zeit" and "die Zeiteinteilung" are feminine and therefore need the pronoun in it's feminine form ("meine Zeiteinteilung", "meine Zeit")