For Germany North Sea and Baltic Sea:
Baltic sea IOW
Baltic Sea Bathymetry Database Mark an area and download.
North Sea AufMod sorry only german.
Alle morphologischen Produkte des Funktionalen Bodenmodells stehen über einen FTP-Server zur freien Nutzung zur Verfügung. Die Polygondaten stehen in der File-Geodatabase AufModDatabasedModelling.gdb über diesen Link bereit:
Die originären Datafiles (50 m * 50 m Modellgitter) stehen hier bereit...
EN: All morphological products of the functional modell could be downloaded via the FTP Server and are free in use.
Polygonal datasets could be found in the AufModDatabasedModelling.gdb this link.
'Orignal' grid file with 50x50m solution (CSV XYZ) could be read from this link.
EDIT comment: I'm not sure for what purpose you need the global data. The GEBCO dataset is good for "global things", but near shore complicated to use. Near shore you are pinned down on regional services.
The matter it self is difficult in terms of "global to handle", because of the financel, political, juristical and commercial nature.
(1) Acqiuring seefloor data in global terms is expensive.
(2) You have a trade-off between, resolution, effort, survey costs and the water depth, which is leading in to a bunch of "incomparable raw data" and relative raw grids (GEBCO 1 min or 30 arc seconds for example).
(3) Data assimilation and usage (terms of rights holder, territorical access) is complicated due to global nature of different souverenity/trading/commercial systems.
(4) This will lead into a political agreement to get data from regions or the world (EU/ US/ UNO bundled under GEBCO f.e.) to assimilate the stuff with a more or less common resolution.
(5) Datasets are very precise if you deal with "regional data sources" (like BSH data set 100 m is a high resolution in bathymetry terms)
(6) IMO you have to handle these trade-off, to use these precise data, fitting to your application using your own assimilation approach (shallow water regions for example) or use the common resolution of the assimilated data products GEBCO.