Is there any relationship between the Commercial Press and the Capital Tongwen Library?

It doesn’t matter.

The Commercial Press (CP) is the oldest publishing organization in China's publishing industry. It was founded in Shanghai in 1897 and moved to Beijing in 1954. Together with Peking University, it is also known as the “Twin Stars of Modern Chinese Culture”.

Tongwen Hall is mainly a "Westernization School" for training translators. Initially, it only had three classes: English, French, and Russian. Later, it gradually added German, Japanese, astronomy, and arithmetic classes.

Later it was merged into the Capital University, which later became Peking University