Why doesn't sea level show seasonality?
Sea level has a strong seasonal signal. The annual variability is less than the daily changes associated with tidal forcing in most locations, but still can be on the order of 5-10 cm (maximum values about 15 cm). 

The causes of the seasonal fluctuations are mostly associated with seasonal changes in wind intensity and patterns, changes in temperature that relate to thermal expansion, and in salinity (haline contraction) and river discharge fluctuations. The annual sea level cycle is only partially related to ice melt and this effect tends to be quite local. 

The largest sea level seasonal cycles are associated with areas in the vicinity of large rivers with strong seasonal cycles (e.g., Bay of Bengal). Also, there is a lot of spatial variability in the seasonal cycle with the northern hemisphere having a larger signal (likely caused by the stronger seasonality in wind patterns).

An example of the seasonal cycle can be seen in the monthly data from the Permanent Service for Mean Sea Level (PSMSL) for Woods Hole, MA (USA) (in m offset to avoid negative values in the PSMSL database). The monthly data shows strong seasonal variability and also a clear trend. As the data is monthly averaged, the tidal oscillations are filtered out. Most sea level rise graphs tend to use annual data and thus the seasonal information is not included.