Is considering events that occur as being by God's will and wisdom, intended as a trial for the servant, and consequently avoiding transgressions based on that, an innovation (bid'ah)? And what is the Sunni alternative?

Everything that occurs in the universe happens by Allah's decree and destiny, as Allah Almighty says: "Indeed, We have created all things with a [divine] decree," and the Prophet, peace and blessings be upon him, said: "Allah wrote the decrees of creation fifty thousand years before He created the heavens and the earth." Trials ( ابتلاء ) come through religious commands and prohibitions, and Allah tests humans with trials and sins so they may repent, for sin and forgetfulness are inherent to humanity. Humans are composed of desire and anger, and these determine their destiny between the highest of the high and the lowest of the low. This composition is essential for the purpose of divine wisdom. There is no harm in perceiving that what happens is by Allah's will and that it is a trial that necessitates obedience to Him, especially if it helps one to stay away from sins.