Bootable Sonoma will not install Sonoma in recovery mode

What is the exact model of your Mac? You can get this information by clicking the Apple menu and selecting "About This Mac".

How did you create the bootable macOS Sonoma USB installer?

The following Apple article is the only reliable method for creating bootable macOS USB installers:

Create a bootable installer for macOS - Apple Support

And the exact model of your Mac?

Oh, and to install an older version of macOS you will need to perform a clean install which involves first erasing the disk followed by installing the OS (Sonoma in your case). Then restoring your data from a backup made before the upgrade to Sequoia since some data stored in Libraries may not be compatible with Sonoma. If you have modified documents after the upgrade to Sequoia, then you will need to manually retrieve those items from the backup, but avoid restoring the actual Libraries.

Here are two Apple articles for erasing the disk (this is one reason why knowing the exact model is so critical for support):

Use Disk Utility to erase a Mac with Apple silicon - Apple Support

Use Disk Utility to erase an Intel-based Mac - Apple Support

To Downgrade from Sequoia macOS 15, on an Apple Silicon Computer, to macOS 14 Sonoma ?

It is doable but not supported by Apple - full stop

If the computer Originally Shipped with macOS 15 Sequoia - it will not be possible to downgrade - full stop

Should the computer have come with Ventura or Sonoma - it is possible to downgrade

ALL CREDIT to @Barney-15E for the Copy and Past below

Just substitute the Sonoma to Ventura to Sequoia to Sonoma

This article indicates it will reinstall the most recently installed version. That has to do with the fact that you cannot completely erase an Apple Silicon Mac. How to reinstall macOS - Apple Support

You will likely need to create a bootable USB installer of Monterey, startup from that, and remove the System Volume with the Disk Utility on that installer.

Create a bootable installer for macOS - Apple Support

These are the steps to follow to erase your Mac's System volume: Use Disk Utility to erase a Mac with Apple silicon - Apple Support.

You will need to Migrate your data from a Time Machine backup as the old Data volume will neither work with Monterey nor will it be connected to the new System Volume.

If you do not have a backup from when it was running Monterey, you cannot use Migration Assistant. You will have to manually move your data to another drive, then move it back to the Monterey Data volume. You may have to export all images from Photos, then import them into the older version, but you can try just moving the Library and see if it will work.