Learn Spanish (Latin America): La cama es blanda, pero pequeña.

Yes! Just like the English word but, pero can link two full sentences, but it can also simply connect two contrasting adjectives, like blanda (soft) and pequeña (small) here.

Could I say pero es pequeña instead of just pero pequeña?

Absolutely. Adding the verb es (is) makes it pero es pequeña (but it is small), which is completely correct. Dropping the repeated verb just makes the sentence a bit shorter and more natural, exactly as we do in English.

Why do we use es instead of está to say the bed is soft?

We use es (from the verb ser) because being soft and small are built-in physical characteristics of this bed. You use ser to describe permanent traits, rather than estar, which is for temporary states or locations.

Why do both blanda and pequeña end in -a?

Adjectives have to match the gender of the noun they describe. Because la cama (the bed) is a feminine noun, both of the describing words must also be in their feminine form, ending in -a.