Were the Jews waging wars and seeking victory through the advent of Prophet Muhammad, peace and blessings be upon him, to defeat their enemies, then disbelieved in him, thinking he would be from the Children of Israel, and was this the reason for the people of Medina's belief in him?

Yes, it is established that the Jews used to proclaim the advent of Prophet Muhammad, peace and blessings be upon him, and sought victory through his coming over the people of Medina. Allah the Almighty mentioned this about them in the Holy Quran, in Surat Al-Baqarah, verse 89: (And when there came to them a Book from Allah, confirming that which was with them - although before they used to pray for victory against those who disbelieved - but when there came to them that which they recognized, they disbelieved in it; so the curse of Allah is upon the disbelievers.)

The stories of Abdullah ibn Salam's conversion to Islam and the testimonies of the Jews before the advent of the Prophet showed that they knew about the imminent appearance of a prophet. In fact, they used this knowledge to threaten their adversaries, but they disbelieved in him out of envy and transgression when the truth, which they recognized, came to them.