Shall I review a paper for my advisor?
One way to resolve this would be that your advisor refused to review the manuscript and suggests you as a possible reviewer. Then the editor can decide what to do. Do not overthink why your advisor was chosen first. He has been around for a longer time and is therefore more known to editors.
I would prefer this procedure to a simple 'yes' to the request (which would be the easy and probably common approach) because it makes contributions transparent. You made a good start with making yourself the corresponding author of your own paper, so it would be consistent if you sticked to this path.
Addition after comment: The answer above makes most sense if you already know how to handle a paper review resulting in a high quality report. Should you require some general support on this, asking your advisor to do the review together and communicate this accordingly to the editor is a possible and viable alternative.
Normally the answer to such requests is yes. It is good experience. But the review may wind up being in the name of the advisor. He was contacted as a more senior academic, I think, and the editor didn't know of his lack of specific knowledge.
However, since the work is related to your own, it might be worth letting the editor know, directly or, preferably, through the advisor, that you have been asked to do this on his behalf. The editor can then act with full knowledge. The advisor would be wise, I think, to review anything you write and give you advice on it.
But journals look for both expertise (which you have) and to avoid conflicts of interest, which could possibly be an issue here. At a minimum, explore this with your advisor, pointing out the issues.
There is no reason to feel bad, especially if you are relatively unknown at this point in your career. The advisor may also have reviewed other things successfully for them in the past.
I would suggest to review the paper, it's a very good experience. Tell your supervisor to warn the journal editor that he refused to review the paper and you will do the work.