my macbook air M1 will not stay turned off

In addition to @SergZak's excellent advice, you also not connect or disconnect anything from the laptop after putting it to sleep or powering it off (including the power adapter) as that could also trigger the laptop to power back on again.

Disconnect all external devices prior to shutting down the Mac just in case one of those external devices is causing a problem.

If none of these things are the reason, then most likely your laptop has a hardware issue of some sort that will need to be repaired.

You can try a DFU Firmware Revive which resets the secure enclave chip & system firmware....I doubt this will help, but it doesn't hurt to try. This should not affect any data on the internal SSD, but if the process fails, then who knows. Unfortunately this process requires access to another Mac running macOS 26 Tahoe (or possibly macOS 15.x Sequoia).

Make sure to have a good backup now while you still can do so. Of course you should always have frequent & regular backups. There are a lot of new ways to lose access to the data stored on the internal SSD of the recent Macs due to all of the hardware, software, and security changes.

Are you touching a key or the trackpad when it is "off" and the screen is black?

Today's MacBooks do not actually "turn off" as in the past. Even though the MacBook is shut down, any keypress, opening of the lid or interaction with the trackpad will immediately bring it back to life power it back on.