Now it turns on then shows me options and Macintosh HD. I tried pressing options, then continue, while giving me 4 choices for the macOS recovery. 1. Restore from the time machine (no files found to restore) 2. Reinstall macOS Sequioa (not enough storage available) 3. Safari 4. Disk utility
You could try the Disk Utility option to check for disk damage and potentially repair.
A sudden shutdown without any advisory message can be due to overheating. The system monitors temperature sensors on various components to detect and mitigate temperatures approaching damaging levels. If detected, the system will first clock back the processor to reduce the work the processor is doing. Remember, work produces heat. You can't change thermodynamics!
if the clocking back does not help, the system suddenly shuts down without any alerts. You may have experienced that, and the inability to restart later could indicate the heat damaged something. Have you tried restarting like a hour later to see if the cool-down will allow booting?
My macbook pro 13" m2 chip suddenly turned off while I was watching.
What were you watching? Videos, whether an online clip, streaming, or video-conferencing, are among the highest load you can ask of a computer. How one has the computer arranged during use can make a big difference in overheating.
Apple info on managing laptop temperatures is here:
Keep your Mac laptop within acceptable operating temperatures - Apple Support
The M2 Macbook Pro 13 has one cooling fan but, as nearly as I can tell from Apple service images, no side vents for cool air intake. Most cooling air for a 13-inch Macbook Pro comes in through keyboard and hinge areas. If either are blocked, you get overheating. Using the computer on your lap or on a blanket or pillow without a hard, flat laptop, can compromise the venting the hinge area offers.
If the computer still will not start after a full cooldown, them what reamsi is Leroy;s sounds advice to seek service/