What is the logical and Sharia-based evidence from the Qur’an and Sunnah for the obligation to make up all prayers missed since the age of puberty?

Whoever embraces Islam after reaching puberty is not obliged to make up the prayers they missed while in a state of disbelief. This is by consensus regarding the original disbeliever, and the preponderant opinion is that it also includes the apostate, because Islam wipes away what came before it. This is also based on the Almighty's saying: {Say to those who disbelieve, if they cease, what has passed will be forgiven them}.

As for the Muslim who deliberately abandoned prayer, there is a difference of opinion among scholars regarding the obligation of making it up. Those who deem it obligatory consider it part of complete faith and piety.

One must not delve into rulings of Sharia based on mere personal opinion; rather, one must refer to the people of knowledge.