What is the ruling on my prayer and the ruling on the لحن (melodic/grammatical error) that occurred from me in reciting the Tashahhud, and is this considered among the manifest لحن (al-lahn al-jali) that invalidates the prayer?

The final Tashahhud is a pillar of prayer according to the Shafi'i and Hanbali schools. The word "At-Tahiyyat" must be recited therein. Dropping the shaddah (gemination mark) or opening the letter Haa’ (instead of kasra/i-vowel) is considered a linguistic error (lahn) that invalidates the meaning and renders the prayer unsound according to this madhhab. Nevertheless, repetition of the prayer may not be obligatory if the error occurred due to ignorance. It is incumbent upon a Muslim to learn the rulings of purity (tahara) and prayer to correct their acts of worship.