After discussing with Kevin Feige, Destin Daniel Cretton, director of Legend of Ten Rings, and Shang Chi did not include Doctor strange in his projects.
Marvel Cinematic Universe (MCU) is known for the push and pull of the special appearance in the movies.
Out of all, Doctor Strange (Benedict Cumberbatch) got the most attention for the same. Also, Doctor Strange appears in Spider-Man No way home that will stream at the same time as Shang-Chi. Due to the clash of cameos, the directors may have decided not to put Doctor Strange in the movie. The reason is obvious and signifies that the makers are busy with other things.
Another reason could be Doctor Strange emerging in the latest episode of What If..? In this episode, he will chase the sinful Doctor Strange. The war between the two Doctor Stranges is crucial for MCU characters as it could temporarily cut him.
Occurring simultaneously, several storylines of Marvel studios has made it tough for the producers to incorporate the famous character of Doctor Strange in the brand new projects.
Sadly, Doctor Strange can't be included in these entertainers, but Wong's partner does appear in Shang Chi and Spider-Man 3. During the teaser, Wong can be seen coming out of the holy place through the flying circle. Maybe he is moving towards the battleground of "Shang- Chi that we will be able to find it out after the release.
Moreover, the producers and directors could have worked out the timing of the release of Shang chi and MCU with other projects of Doctor Strange. Nevermind! The movie still holds a lot of interesting stuff that will be revealed on September 3. We can't wait to know. What about you?