Usually, for European languages, copulas are considered intransitive. They do not have objects in any European language. (Some African languages, however, do seem to have their copulas be properly transitive).
OK, hey... wait a sec. What's the thing that goes on the right side of 'is' then, if not an object? Isn't SVO the rule of the day in English? Let us call the noun that typically is on the right-hand side of a verb the ... 'right-hand noun'. However, do not take this to mean that the 'right-hand noun' has to be on the right hand of the verb.
Objects have more properties than being right-hand nouns! These properties enable us to make tests for determining whether something is an object or not. One thing you can do to objects in English, that you can't do to other things, is turn them into the subjects of passive verbs (Note: some speakers can do this to indirect objects too). So,
he kicked the ball → the ball was kickedNearly no speakers, however, will permit
he was the CEO of ACME Industries →(This might happen in modern poetry, however, but modern poetry intentionally violates grammatical patterns on occasion)
the CEO of ACME Industries was been by him
Another thing English permits is coordinating objects of different verbs:
he saw him and acknowledged him →
he saw and acknowledged the man
Try this with a typical transitive verb ('saw', for instance) and a typical copula ('was') and you'll find a problem.
*he was and saw a man
*he saw and was the man in the mirror
I imagine these may appear in poetry, but they feel weird and at the very least will fail to be considered grammatically well-formed by most speakers.
However... you can coordinate the right-hand noun of 'to be' with the right-hand noun of some other verbs:
he suddenly became, and maybe still is, a good chess player
Another test which English kinda-sorta lets us do, but which is bad for a variety of reasons, is case assignment.
Some speakers require the nominative for right-hand nouns of copulas:
"it is I".This seems inconsistently applied, though, and I bet it's rather associated with the particular verb × person pairing, i.e. the same person may have
"it is I", but "it is him!",or
"it is he" but "the stem cells that became him".In English, apparently, for some speakers, the accusative case is tied to the right-hand noun, rather than to objecthood. English case assignment is inconsistent from speaker to speaker, and even for speakers it is inconsistent from verb to verb, and even for speakers may be inconsistent with the same verb from person to person.
What we further can notice, is that the copula can take arguments that are not nouns, but are e.g. adjectives or adverbs or prepositional phrases, and these are still as closely tied to the subject as would a right-hand noun be. It can take 'red', whereas a transitive verb usually takes 'a red one'. (With weird exceptions like 'see red', which basically is sorta intransitive, since it rather just encodes 'to rage' or somesuch - i.e. 'red' in 'see red' does not really have an actual referent!)
Summary: in very many languages, verbs can take noun arguments that are not objects. Assuming that a verb is transitive just because there is a noun in the same position that an object would normally go does not necessarily work out, and a verb is not necessarily transitive just because it lets you do NOUN VERB NOUN.
Exceptions, however, exist, and in several African languages apparently 'to be' is indeed transitive in the sense that the 'right-hand noun' in fact passes objecthood tests in these languages.