Why not null?

Wouldn't it be more convenient to have a path to the key?

Can we split this up into steps so we can give better error messages?

This should work the same way WNS works. There's a get and set method, and a convenience method that combines the two.

what does iat mean?

Seems presumptuous to hardcode that

I prefer the log message split out, rather than a multiline function call

ditto

int isn't nullable. Like this the default value is 0 because it will be cast to int.

@return $this

should probably be static instead of self

@return $this

I understand why we would want client_email and private_key properties, since that is static info that won't change (most likely). But the oauth lifetime seems flexible. I think we can leave that as parameter to the method.

try to not use withConsecutive in new code

What format should I think of here? Timestamp?

What is a client_email? Is it a project identifier? A username?

Won't these two show exactly the same in the log?

I think this is safe to have a reasonable fallback.

Why these?

Can you group these with the other small functions?

Nope

I don't think we need to log this. The exception is good enough here, it just shouldn't be an UnexpectedValueException. We already use that below and the case here would need to be handled differently.

That's not "good form". If you need info from the previous exception, you should attach the previous exception, not concatenate the messages.
new RuntimeException('message', 0, $e);

Why not static like the others?

@see might be better for this

Can you make the time a constant? I'd never know to look for it here.

Please use the constant here

Optionally, this could be:
$http_response->status_code = $http_code ?? NULL;

Ship It!