I also used the "Bulletin" tone as a custom text sound for specific contacts and was disappointed when the tone was not available after iOS 17 update. If you don't want to wait and see if Apple re-adds it in a future update (which may or may not happen), you can always create the tone with GarageBand and export it as a ringtone and it will then be selectable as a tone. This is what I did.
If you are interested in doing so and are not familiar with using GarageBand (like I was), then you can watch the YouTube video "How To Add Custom Notification Sounds On iPhone" by WebPro Education to see how to create the tone and export it as a ringtone.
I found the tone on zedge.net and downloaded it and it automatically saved it in the "Downloads" folder of the "Files" app on my iPhone. When I used GarageBand to load the sound file, I selected the "Files" tab and then selected "Browse items from the Files app" and selected On My iPhone and then Browse and under Favorites was the Downloads folder with the downloaded sound file. I imported the file into GarageBand and then exported it as a ringtone and now it is available under Sounds & Haptics (or when editing Contacts for personal tones) to be assigned as a text tone.
There was one thing that I found in GarageBand that was not covered in the YouTube video and that is there is a triangle symbol next to the red record button (when using Audio Recorder). Make sure the triangle symbol is white and not blue. If it is blue, then there will be a constant tapping sound (like to keep a beat) in addition to the bulletin tone. If the triangle symbol is white, then there is no tapping sound.