Hello tijlv,
Thank you for posting in the Apple Support Communities. We understand that alarms appear louder than ringtones, and we're here to help.
As it turns out, there isn't a separate setting to adjust the alarm volume. However, to isolate this issue further, we suggest considering whether Attention Aware Features is enabled and causing the ringtone to appear quieter than your alarm. To check if this feature is on, tap on Settings > Face ID & Passcode > Attention Aware Features.
Change Face ID and attention settings on iPhone
If you discover that Attention Aware Features is causing the ringtone to appear quieter than the alarm, then we recommend either turning off Attention Aware Features or adjusting your system sounds. The Apple Support article below explains how to adjust sound settings:
Change iPhone sounds and vibrations
We hope this information is useful. Kind regards.