Is 'be' in 'be going to' an auxiliary?

This is the auxiliary "to be" that is used to indicate present continuous

This is the standard use of the present present participle with the auxiliary "to be".

I am writing.

You are asking.

He is commenting.

She is going.

etc.

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Example

John: Where are you going?

Ann: I am going to town to do some shopping. (present continuous)

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Indicating the future

Of course "going to" can also be used as a way of telling the future. But the grammar is still the same and "to be" is still the exact same auxiliary verb.

John: Where will you be going on your day off? (future is indicated by "will")

Ann: I am going to go to town to do some clothes shopping. (future is indicated by "am going to", which is the present continuous of "to go to")