Traveling to US for only 4 days. What will happen with Biden's mandatory quarantine?

tl;dr version

You can probably get away with what you are planning. But if you choose to do so I will consider you to be the sort of person who does not care for the wellbeing of yourself or (more importantly) other people around you.

Long version

Biden's executive order can be found here

In the case of the OP the relevant paragraph is probably:

Sec. 5. International Travel.

..

(ii) required to comply with other applicable CDC guidelines concerning international travel, including recommended periods of self-quarantine or self-isolation after entry into the United States.

The CDC recommendations can be found here. The CDC only recommends quarantine:

If you participated in higher-risk activities during your international travel

Which are listed as (my emphasis):

• Travel from a country or U.S. territory with a Level 2, Level 3, or Level 4 Travel Health Notice.

• Going to a large social gathering like a wedding, funeral, or party.

• Attending a mass gathering like a sporting event, concert, or parade.

• Being in crowds like in restaurants, bars, fitness centers, or movie theaters.

• Taking public transportation like trains or buses or being in transportation hubs like airports.

• Traveling on a cruise ship or river boat.

But the site also says

You may have been exposed to COVID-19 on your travels. You may feel well and not have any symptoms, but you can be contagious without symptoms and spread the virus to others. You and your travel companions (including children) pose a risk to your family, friends, and community for 14 days after you travel.

At this point I'll point out that a negative PCR test only shows you were negative (within the bounds of the accuracy of the test) at the time you took the test. So there is scope for being infected after you have taken your test, and the more people you are around, the higher the chance of encountering someone who could infect you.

The CDC site also says

Always follow state and local recommendations or requirements related to travel.

My state has mandatory 14 day quarantine for any out of state visitors. And the penalty for breaking that quarantine can be:

Non-compliant individuals are subject to involuntary quarantine by the New Mexico Department of Health under the Public Health Emergency Response Act.

So at the Federal and CDC level they talk about recommendations only. At the state level it becomes more strict and there can be actual penalties.

But no one that I know of is currently suggesting GPS monitoring (a la Cayman Islands) for the US. So adhering to the restrictions is up to you to follow. However last year at least some tourists in Hawaii were arrested for breaking local quarantine restrictions.