That issue should be discussed openly.
ように is the broader, everyday way to say 'in the manner of' or 'as', while 通り in this sense usually follows a specific plan, instruction, or quoted statement to mean 'exactly as stated'.
invisibly; secretly; privately
openly and covertly; publicly and privately; implicitly and explicitly
From 陽 (yang, positive, open) + adverbial particle に. The kanji 陽 carries the sense of openness and visibility, contrasting with 陰 (yin, hidden).