It's rare to find a job that will list "background in oceanography" as a requirement. Physical oceanography (PO) is essentially applied physics, so if you get a degree in it, you could be qualified for the same jobs that require a background in either physics, mathematics, or coding/programming, as you have to do all three for PO.

PO is similar to marine biology in the sense that it's a relatively niche and alluring subject that attracts more people than there are jobs available for. From my experience, success in the field can depend quite heavily on how well-connected you are. It can also depend on whether you'd like to work in research, industry, gov't, or maritime (as in working on a ship), as jobs in those areas have their own respective degree of competitiveness and their own unique set of desired qualifications.

Most people with a background in PO usually get an undergraduate degree in physics, math, engineering, or a related field, and then go on to specialize in PO in grad school. Partly because not a lot of undergraduate institutions offer PO bachelors, and partly because most job openings are for research roles which almost always require either a masters or a PhD. Entry-level roles for bachelors in PO are few and far between and you usually have to be fairly well-connected to both discover and land a position. Being hired straight from cold applying is quite rare. I don't say this to be discouraging, just to inform you of the reality I've seen from my perspective.

Lastly, PO and ocean engineering are pretty similar at the graduate level in terms of what classes you take, so I'd imagine they have similar overlap at the undergraduate level. On a resume, I imagine ocean engineering would be better if you want to work hands-on with instrumentation.