أحسن الله إليكم، In Dhuhr or ‘Asr, if the imam goes into rukūʿ while I am reciting a surah (after al-Fātiḥah), should I stop and follow him immediately or finish the āyah first? جزاكم الله خيرًا

Follow him, the surah after al-Fatihah is only a sunnah while following the imam is obligatory. If you are on the last words of a short ayah and you are certain you will still reach the ruku with him, finishing it is not lagging behind.