What can I do to make myself stand out in the job market during this COVID-19 period?

I don't think the COVID-19 context affects the top performers much (certain industries excluded). No matter how bad the situation turns, the company will not cut its stars unless it goes bankrupt.

I have team members facing similar situation as you. They have good attitude but are not outstanding. My suggestion is if you are not super book smart, focus on your biggest strength and make sure no one (at least in your company) can beat you in this area. In that sense, you make yourself indispensible.

I'm one of those "book smart guys" with full scholarship from undergrad till PhD. My personal experience is it's way more a matter of consistent affort than being "smart".

Currently no matter how much you stand out, not many companies are hiring.

Except ecommerce, food delivery, and logistic company.

I will give advice to the secondary question:- if you are fresh grad and has no job, go do volunteering work.

When the job market recovers, and instead of a blank slate, you have "volunteering experience" in your resume, you are going to shine more than others.