Thanks for visiting the Apple Support Communities! I understand you don't see your playlists within Apple Music on your iPhone as expected.
If you have your entire music collection available within iTunes on a computer, I suggest to update iCloud Music Library, as outlined in the following guide: Turn on iCloud Music Library
If you don't see your content on all of your devices
On the computer that contains your original music library, make sure that you're signed in to iTunes with the Apple ID that you use with Apple Music and have iCloud Music Library turned on. Then, from the menu bar at the top of your computer screen or the top of the iTunes window, choose File > Library > Update iCloud Music Library.
Make sure that that you have the latest version of iOS, macOS, and iTunes on your devices in order to sign in with the Apple ID that you use with Apple Music.
If you don't have a computer with iTunes available, I suggest to force the Music app to close, restart your iPhone, and then check for your playlists: How to force an app to close on your iPhone, iPad, or iPod touch & Restart your iPhone, iPad, or iPod touch
If the behavior continues, I suggest to turn off iCloud Music Library on your iPhone, enable iCloud Music Library, and then test the behavior. Keep in mind, turning off iCloud Music Library will remove music which has been downloaded for offline listening. You can see those steps from the following guide: Get help with iCloud Music Library
Turn iCloud Music Library off, then on again
On your iPhone, iPad, or iPod touch:
- Go to Settings > Music, then tap iCloud Music Library to turn it off.
- Close Settings.
- Go to Settings > Music, then tap iCloud Music Library to turn it on.
If you have content downloaded to your device, it deletes from your device when you turn off iCloud Music Library. After you turn iCloud Music Library back on, you can redownload the content.
Let me know how it goes from here.
Kind regards.