Should one interrupt prayer or continue with it if the muezzin calls the adhan for the next prayer before the completion of the first rak'ah, knowing that I began the prayer at its very last moment due to some circumstance?

Whoever catches one raka'ah of the prayer has caught the prayer. It is not permissible to interrupt a prayer even if the time for another prayer has begun. Rather, the first prayer must be given precedence due to the obligation of sequential order according to the majority of scholars. It is not permissible to delay a prayer beyond its preferred time except for an excuse like sleep or forgetfulness. Whoever delays it without an excuse has committed a grave sin, based on the words of Allah Almighty: "So woe to those who pray those who are heedless of their prayer."