When someone is watching me pray, I suddenly become more careful and beautiful in my salah. Does that mean my private prayer, done carelessly, exposes the truth of my heart?

What you have noticed about yourself is not a verdict passed against you. It is information, and useful information, because it shows you exactly where the work lies.

Start with what is certain. Your Lord is nearer to you than you can picture, and nothing in you is hidden from Him, whether people are watching or you are entirely alone.

“And We have certainly created man, and We know what his soul whispers to him, and We are closer to him than his jugular vein.”

Qur’an, Qaf 50:16 · meaning

Since He is always near and always seeing, the Prophet, peace be upon him, showed us how to close the gap between the watched prayer and the private one. The way is not to pray worse in front of people, but to feel Him near in every prayer.

“It is that you worship Allah as though you see Him, and though you do not see Him, He surely sees you.”

The Prophet (peace be upon him), Sahih Muslim (8a) · meaning

As for that small pull toward performing for others, it should be named plainly. The Prophet, peace be upon him, spoke of it more gravely than of almost anything else he feared for those he loved.

“The thing I fear most for you is the lesser shirk,” and when asked what it was, he said, “Showing off.”

The Prophet (peace be upon him), Musnad Ahmad (23630) · meaning

He called it the thing he feared most for us, so it deserves our attention. But the answer to such a warning is not fear and not despair. It is a cure that is within your reach: do not dim the prayer others see, lift the private prayer until it matches, praying alone as carefully as you would in the front row. In time, and by His mercy, the two prayers become one. That this troubles you at all is a sign your heart is already turned toward Him.

One small step: In your next prayer at home, where no eye watches, straighten your posture and slow one sajdah, as carefully as if you stood in the front row, offering that hidden care to Allah alone.