Jesus adhered to the Hebrew religion and comfortably stayed within that tradition. His emphasis on 'silent' prayer, was simply in contradistinction to the hypocritical performative prayer of certain religious leaders that did not come from pure motives. The reason why prayer was silent, was not because it was in any way meant to be a mystical eastern style meditative experience leading to some kind of emotional ecstasy or zen or any other psychological manifestation, but rather because it was meant to emphasise the true goal of prayer i.e. maintaining a personal relationship with God through verbal communication.
Believers were encouraged to approach God like they would a friend or father and speak to him about their lives and not consider their human needs too lowly to concern a deity. Eastern meditation on the other hand is characterised by emptying of the mind, the polar opposite of how Jesus taught his disciples to pray. Jews and Christians throughout history have believed that on the other end of a prayer is a personal God who is responsive to our petitions whereas buddhism has no concept of a personal God but instead concerns itself merely with the human mind. For Jews and Christians the efficacy or power is not in the act of praying, but in the voluntary act of God. For Zen buddhists the efficacy or power is inherent in the act of meditation.
Communal prayer was still considered appropriate and was encouraged, Jesus just didn't want anyone showing off to their religious friends as a means to gain status without truly caring about God, His righteousness, etc.
Prayer by itself was also not considered a method to discover truth. There is a heavy emphasis on seeking truth in the study of the word of God which runs throughout Jesus' teachings, which was already present in Judaism and continues to this day in Christianity. The desert fathers, as well as mystical sects in judaism and islam are outliers, and their religious practices are amalgamations of mystical traditions of other religions with their respective host religion (christianity, islam, judaism). Theirs is a religious phenomenology that draws on the religious verbiage and concepts of a familiar religion, without concerning itself with the authoritative source of said religion, but rather with seeking a mystical experience.
It is not just literalists and evangelicals that consider eastern style meditation and associated religious concepts as foreign to mainstream historical christianity and judaism, it's most reputable scholars in the fields of NT studies, Church History, etc.