Hungry is here used as an adjective. In the case of the verb be, it takes substantives (nouns or pronouns) or adjectives in its predicate complement, NOT adverbs. You cannot say “I am *soon.” or “I am *often.” as complete sentences with a period/full stop following: both those are wrong.
This is because you cannot use an adverb to modify be any more than you can use an adverb to modify a pronoun. Sure, you can use intensifiers, like saying I really am, but an intensifier isn’t exactly in the same class as an adverb. Plus there has been something left out at the end that’s to be understood as the target of the intensifier.
Sometimes people will get all tangled up about things like “I’m here” or “I’m there” or “I’m home”, but that all works differently: it’s not actually an adverb there. It’s some kind of substantive. Sometimes it’s more of a locative pronoun as with here or there or a temporal one like now or then.1
At other times it’s a normal noun used as an adverbial phrase in of itself, like tomorrow or home. “Adverb” is something of a grab-bag category into which the weak-willed toss anything they don’t much know what to do with.
As for the other examples apart from hungry, those are NOT adjectives: they are clearly adverbs because they are modifying a verb. It doesn’t matter what they look like, and it doesn’t matter what one or another dictionary says that they “are”. All that matters is what they happen to be doing here and now, and here and now they are modifying verbs.
Remember this: Just as not all words that end in -ly are adverbs, not all adverbs end in -ly.
If one person runs FASTER than the second person, then the second person runs SLOWER the first. If you dig down DEEPER, you will find that adverbs aren’t bound by any such -ly restrictions, be those in the positive degree, the comparative, or the superlative.
The SOONER you are brought to understand this, the SOUNDER you will sleep.
- There’s a fancy word for these types of words — deictic — but it isn’t one they teach in grammar school and I don’t want to confuse anyone.