seem is a type of verb known as a link verb. A link word can be followed either by a noun or an adjective:
she seems intelligent - adjective
she seems an intelligent woman - noun phrase
These are just two ways of expressing the same meaning.
In both of your sentences, disappointed is a passive participle- a special kind of adjective.
The words seem and appear are special link-words: we can also use them with to be + an adjective. Some other link words are also used informally in this way, for example look, get, and grow.
she seems disappointed - adjective
she seems to be disappointed - to be + adjective
These sentences have different constructions but identical meanings.
He seemed to becoming disappointed.
This sentence is nearly grammatically correct: here are two alternative corrections, both meaning that at some time in the past his mood changed from not disappointed to disappointed
He seemed to become disappointed. - simple
He seemed to be becoming disappointed. - continuous