Do I need to have taken physics in high school to major in bioengineering at a top tier university?

You need to ask your high school.

But, generally for college applications, you self-report your in progress and planned courses. They are then verified by your final transcripts when you send them to the college you matriculate to.

Physics is a required class for any science major. Not having a high school leve course in the subject is a huge red flag. The difference is in biochem you only have two classes (equivalent to two super intense AP classes, so a basic HS introduction is still expected) but anything involving engineering involves a lot more.
Basically you need to take a physics class.

Do you think listing it in my additional information and self reported winter/spring courses will help? Or mentioning any 8-12 week course I choose to take now online?

Spring courses have no progress to report.
The first issue is getting an admit. Second is whether you’re prepared once there.

What colleges?

What are your stats? Where are you aiming? And why not call it biochem? Are your stats and stem ECs competitive for your targets? Much we don’t know.

You took a nice science sequence. As stated, State in one line why. Getting some physics would be great. As stated try doing it online etc. If not at least a community College course either next semester or over the summer if allowed. I wouldn’t lose my head trying to get it in now. Call the admissions of some colleges you are applying to for advice. Follow that advice.

I’m probably gonna major in biochem now. Stanford, Penn, Brown, Duke, Yale, Northwestern, JHU, Rice, and Pomona are amongst my top choices. Also applying to UCB, UCLA, UMich, UWash, WashU, Bowdoin, Tufts (and maybe Harvard bc why not haha)
1570 SAT, 4.0 UW GPA with 10 APs over 4 years
founded science as service club (expose students to outside the classroom topics, workshops for younger kids, annual service project each year, planning school’s first STEM Night for Nov.), president of Science Olympiad with several regional/invitational medals, amongst top in competitive region, trying to get to states this year! (anatomy, microbiology, chemistry), VP of special needs club (plan dance for 200+ ppl every year), VP of Tech for NHS, science camp counselor this summer, COSMOS Biomedical Sciences last summer, XC/track captain (top 10 team in CA state for xc), bioengineering science fair project junior year (2nd in silicon valley), 3 time state and national FBLA speaking competitor (recently 1st at states, 3rd at nationals), self-employed tutor, YMCA swim instructor… I think that’s about it.

Are you instate for CA?
What’s your budget?
Yes, you list Spring and online classes on you SRAR (or your 12th grade list of courses in CommonApp).

“and maybe Harvard bc why not haha”

“Because Why” is really the question you ask yourself for any school. There are plenty of reasons not to attend highly ranked schools. UCB has the largest classes in the US and undergrads are tasked with teaching other undergrads at Harvard to cite two examples.

The schools on your list are VERY different, unified by a single thing, reputation. Dig deeper. It’s your 4 years and your family’s money.

Choose wisely whether you apply in engineering or science. It may not be easy to transfer from one college to another within a university. Moving majors within the college of engineering or arts and sciences will be easier.

BE is very physics based in both medical devices and imaging fields. You should decide if you like and are proficient at physics. It is also easier to transfer out of engineering than from science to engineering.

A top tier school freshman curriculum will require prior physics knowledge. Chem 1 engineering sections may contain a lot of quantum chem. When you gain the knowledge in HS, may not be as important as deciding if you enjoy physics.

Make sure you take Physics at the community college so it is on some transcript. Unless it is normal for all other students in your highschool to take Physics, it shouldn’t hurt you.