How can I replace the seat on my wall-mounted toilet
You need to identify the toilet.   There is often a brand logo under the toilet seat, between the bolt holes.
That said, it appears to be a Duravit “darling new” wall toilet.  There are two or three models within the range, each gets its own seat/cover.  Measure the length of the top of the bowl from wall to front edge and it will correspond with the spec online at www.duravit.us.   It looks like the elongated version which probably uses toilet seat 0063390000, but you should check.
Good luck!