I have the feeling I miss / don't understand something conceptually. I
would like to understand why lily refuses to engrave the slur of the
first fis.
On the question of why the first tie does not appear: there is a note
(a2) in the voice between the first and second fis1 that interrupts the
tie. This can be resolved with tieWaitForNote.
\set tieWaitForNote=##t fis1 ~ \unset tieWaitForNote fis ~ etc,
as explained in
https://lilypond.org/doc/v2.24/Documentation/notation/writing-rhythms#ties.
--
Timothy Lanfear, Bristol, UK.