Is it obligatory for one who intends to embrace Islam to repent from showing off (riyaa'), and is one considered a Muslim if they repent from major shirk but remain determined to show off?

One must completely repel and ignore misgivings (waswas). The Islam of one who embraces Islam with sincerity in the Oneness of Allah Almighty is accepted, and he must fulfill religious obligations and abstain from prohibited acts like showing off (riya').