unable to enter boot manager after hold down Option Key at startup

So when you hold down the Option key immediately after hearing the Startup Chime (timing can be critical as @WheelieNick mentions since holding it too soon or too late can cause the key press to be ignored).....you don't see the Apple boot picker menu?

If you don't see the Apple boot picker menu & the system just boots normally, then there is some sort of hardware issue.

If you see the Apple boot picker menu, do you see an option called something like "Install Big Sur"?

How did you create the bootable USB stick?

Have you tried using another USB stick?

If the Mac is unable to boot from the external drive, then it will sometimes just boot right into the default boot drive which is typically the internal drive.

Try disconnecting all other external devices from the laptop & connect the USB stick directly to the laptop. Try using the other USB port as well. The USB port on the right side is part of the Logic Board, while the port on the left is on a separate I/O Board.

Are you certain that the keyboard works properly?

Press and hold the option key as soon as you hear the startup chime.

If that doesn’t work then you might try again with the other option key or with a USB keyboard plugged into the laptop.

Successfully booting into the boot manager often comes down to timing. Pressing and holding the option key at the same time you press the power button may or may not work. I have always had my best success if I press it immediately when I hear the chime.

For the 2024 MacBook air Big Sur is not supported anyway. Make a apple silicon bootable stick with Sonoma or Seqouia and try again