As a learner I would say, in your two sentences the verb is the linking verb is. After linking verbs you can use either an adjective or a noun phrase. The important thing is that a past participle can play three main different roles:
- they can be an adjective (both attributive and predicative)
For example, this book is invaluable; here invaluable is an adjective. Similarly you can say: He is an old and trusted friend.
- they can be used to form a verb phrase
For example, New buildings are constructed by the company.
- they can be used in adverbial clauses, adjectival clauses, and phrases
For example, Having walked for a while, he returned to the house.
In your question, the branded and trusted are adjectives.
Moreover, I think it is important to mention that the superlative and comparative forms for such adjectives are constructed using most and more.