Audiveris -> MusicXML -> MuseScore

"Suis-je à la bonne place pour demander conseil ?"

Yes, there are users in this forum who have experience of Optical Music Recognition (OMR). You will probably get answers both about the Audiveris (free) OMR and about other OMR products (commercial).

I think that your problem is simply that the print quality of your PDF score (O, Du Fröhliche) is too bad for any OMR system to process correctly. My guess is that this PDF was scanned from a photocopy of a photocopy of a photocopy...? Look at the black noteheads: these are not dense enough and they have many "pinholes" of grey or white:

I am a keen user of OMR (SharpEye, PhotoScore etc), but in this case I would probably choose to typeset this short piece directly in MuseScore. It will be much quicker to typeset than to try to correct all the OMR mistakes: missing time signatures, missing notes, wrong notes, incorrect measure durations... and so on.

"Tout ce casse-tête simplement pour aider une chorale ..."

I do understand your frustration, because I also create practice files (for a church choir). Recently I have started to rely less on OMR, because I have gradually found ways to speed up typesetting in MuseScore.

Here is a link to some practice files which I created on the evening of 20 December.
https://rootham.org/playlist/smb/hon/hon_542_What_child_is_this.html

The process covered these steps:
- typesetting the full SATB score in MuseScore
- saving on my PC four different MSCZ versions for Soprano, Alto, Tenor and Bass practice
- adding instrument sounds in the Mixer appropriate for the separate S A T B practice files
- saving the five MSCZ scores on musescore.com
- finding a YouTube performance of the work
- creating an HTML file to host the embedded MSCZ practice files and the YouTube recording

Two "speed-up" techniques which I use for typesetting are:
1. First copy-and-paste repeated rhythms (e.g. "quarter note, eighth note, quarter note, eighth note" in a 6/8 piece), disregarding the pitch of the notes.
2. Then use Re-pitch mode to correct the pitch of each voice very quickly, because Re-pitch mode preserves the existing rhythm. See the Handbook section about "Note input modes":
https://musescore.org/en/handbook/3/note-input-modes#repitch