Was Siri programmed for rudeness?

It just indicates you are pausing after saying Hey Siri, and you get audible feedback that you are heard. There is not reason to pause after saying Hey Siri, you just need to speak in a continuous sentence. The is most notable for users you are used to Alexa or Google where the delay was needed to make sure the command activated. With Siri, there is no delay needed.

It is the same as if you were talking to your friend and said "Hey Jack", they will respond with something like "uhumm" or "yahh", but if you said "Hey Jack what time is it", they will tell you the time.

While not programmed to be rude, it has been programmed to provide that feedback, when a user pauses between invoking Siri and asking a question. For best results, make your request as one continuous sentence, as in “Hey Siri, what is the temperature”.

And how is doing the same thing people do rude?

If you walk up to someone and say "Hey, John.", and nothing after that, it's a virtual certainly that person is going to say, "What.", or "Yes?", or something similar. The assumption just about every real person on the planet will presume from such an opening statement is you are looking for confirmation of your presence before you will continue to the point.

Siri is doing the same thing when you pause.

It’s a piece of AI, not a living organism. It cannot consciously be “rude” any more that it could consciously be “polite”.