What is the ruling on my feigning prayer after intending to leave it, in order to avoid embarrassing the worshippers? And is my action considered minor or major polytheism (shirk)? And is it obligatory for me to perform ghusl, or is ablution (wudu) and repentance sufficient?

One should turn away from obsessive thoughts and not succumb to them. If someone misses a single pillar with the Imam in the first rak'ah, such as not catching the bowing, this does not justify rejecting or interrupting the prayer. Rather, they should continue with the Imam and make up the missed rak'ah after the Imam says the taslim (definition). Rejecting the intention for prayer or intending to leave it invalidates the prayer. Pretending to pray when the prayer is invalid, out of consideration for other worshippers, is forbidden. If it is done with the intention of showing off, it is minor shirk (definition). What occurred is minor shirk and does not take one out of the fold of Islam, and the ablution is valid. Whoever did this should hasten to repent, seek forgiveness, and turn away from obsessive thoughts.