It seems the confusion here centers around the verb to be, which sometimes serves as an auxiliary verb and other times is the main verb.
When it's an auxiliary verb, the main verb will follow. As you pointed out, to be is used in passive voice structures (in which case the main verb should be in the past participle form), and in continuous tenses (in which case the main verb should be in the present participle, or -ing, form). However, in your example, we see no main verb that follows 'been'.
In any verb construction, the last word is the main verb while the rest are auxiliary verbs (or adverbs). Your verb construction is "have been", so 'have' is the auxiliary verb and 'been' is the main verb. Since to be is not an auxiliary verb in this case, your sentence is neither passive nor continuous.
In their comment, mahmud koya correctly identifies "have been" as present perfect (simple) in the active voice. The present perfect uses 'have' before the main verb in the past participle form: 'been'.
In conclusion, it seems you considered to be only as an auxiliary verb, which left you wondering about the missing main verb. But remember that to be isn't always an auxiliary verb, but can be the main verb, as it is in "there have been many inventions ..." Therefore, you have an active sentence in the present perfect tense.