If I move to Canada with OINP, I understand I need to stay in Ontario, but can I work in a company based outside of Ontario (remotely)? Will there be any issues later with my citizenship application?
Unless the terms of the PNP specifically say that you must
work for an employer based in Ontario, there should be no issue. (And I don't have the information to check, but don't believe it does.)
FYI the tax system in Canada works in such a way that the resident will end up paying taxes in Ontario, so overall Ontario benefits.* That's not to say it's exactly what the province or employers in Ontario want, but I'd put the chances of there being an issue at close to zero.
*The employer will withhold taxes in province X, but the employee pays taxes in Ontario (whatever withheld counts as paid) - neither have to do anything, it all gets worked out by Revenue Canada and the provincial counterpart agencies (the split between them is a bit more complex but no need to worry about that). The employee can still end up owing some extra (or getting a bigger refund) because provinces all do things a bit differently.
**It's possible there's a bit more to it than this esp if one leg is Quebec but overall hudnreds of thousands of people do this and it's not a big deal.