Ceci asked ‘if Allah belongs to the East and the West so why do Muslims only pray facing the East?’
Indeed the East and West belong to Allah.
From a historic perspective, according to the Bible, the Jews and Jesus faced Jerusalem when they prayed. See:
Da 6:10 – Now when Daniel knew that the writing was signed, he went into his house; and his windows being open in his chamber toward Jerusalem, he kneeled upon his knees three times a day, and prayed, and gave thanks before his God, as he did aforetime.
Eze 21:2 – Son of man, set thy face toward Jerusalem, and drop thy word toward the holy places, and prophesy against the land of Israel
More on that here: https://understandingchrist.com/worship-in-the-bible-not-prayer/
In Islam we actually believe that Meccan Kaaba, house of Abraham in the east was prescribed to them in the past and they know this, but they decided to change direction towards Jerusalem. See:
We have certainly seen the turning of your face, [O Muḥammad], toward the heaven, and We will surely turn you to a qiblah with which you will be pleased. So turn your face [i.e., yourself] toward al-Masjid al-Ḥarām.1 And wherever you [believers] are, turn your faces [i.e., yourselves] toward it [in prayer]. Indeed, those who have been given the Scripture [i.e., the Jews and the Christians] well know that it is the truth from their Lord. And Allāh is not unaware of what they do.
Allah is One. Harmony and unity is essential in faith as disorganization is not an option. Imagine people praying together and facing all directions. Not a good look.
Allah chooses which unified direction man should face and can and has changed this.
With the advent of Islam, Allah decided to separate/distinguish Muslims from others. This did not only happen with prayer but other practices like keeping the beard.
With prayer, Allah in His infinite wisdom decided, with the restoration of the Kaaba, known as the house of Abraham, for the faithful to now face that point in prayer.
“So from wherever you go out [for prayer, O Muḥammad], turn your face toward al-Masjid al-Ḥarām, and indeed, it is the truth from your Lord. And Allah is not unaware of what you do.” – Al-Baqarah: 149
However Allah says what means in the Quran, Baqarah 117:
“Righteousness is not that you turn your faces toward the east or the west, but [true] righteousness is [in] one who believes in Allah, the Last Day, the angels, the Book, and the prophets and gives wealth, in spite of love for it, to relatives, orphans, the needy, the traveler, those who ask [for help], and for freeing slaves; [and who] establishes prayer and gives zakah; [those who] fulfill their promise when they promise; and [those who] are patient in poverty and hardship and during battle. Those are the ones who have been true, and it is those who are the righteous.”
So while uniformity is essential, Faith is more than this.
And Allah knows best.