What problem does this address?

The existing Media & Text controls for padding and margin apply to the entire block:

This makes it difficult to use the media block for use-cases where more control is needed within the block, such as:

• controlling the space between the media and the text
  
• having the image span the full height of the block, while ensuring the text has a custom amount of padding.
  

What is your proposed solution?

The introduction of a gap option for the text could help. This would be implemented as a configurable 4-way padding or margin around the text, allowing the user to control:

• how much space there is between the media and the text
• how much space there is between the text and the other horizontal edge
• how much space there is between the text and the top/bottom of the block

An alternative would be having a separate padding controls for the media and the text: