I've had a similar project with bridge new bridge foundations (twinning of the existing 2-lane hwy) adjacent to existing bridge foundations - spread foundations. Soft soils, according to the soils report, for a couple of metres below design level. How was it played by the designer? He ignored it. So far, okay . . . but, then again, no one is monitoring the settlement. I certainly don't as it might help the contractor - I don't represent him!!!
I agree that you draw up all your footings to scale in both plan and in a number of sections. Mark on the existing foundations - type, etc. (spread or piled). Mark on existing ground surfaces and FRL (final road level). Determine stresses caused by new embankment and, also important, the bearing pressures under abutment (especially if spread foundations). See how pressures interact within/beneath your existing structure. If you have soft compressible soils under existing, don't forget that the new stresses may induce more downdrag forces. Also, don't forget the "other side". In our case, the distance between the abutments is only 8m. Instead of a box bridge, they used individual spread foundations - the toes were only 3m apart. So - you might have two or three other factors from the other side having an influence as well.
Once you have established the above, then you can look at possible measures to alleviate - one of which may be your sheet pile wall - or, perhaps, a secant pile wall, or, if the geometry is right, maybe you might want to connect all the pieces together.
Hope this gives some additional insights.