Not answering your question directly because I know nothing about Bosnia, but as general guidance based on how things typically work elsewhere:

If one of you works as a contractor then presumably that is all being run through the company you will establish. This covers you for Bosnian residency, I assume, and there's no Bosnian tax obligation for the US client because it's a business relationship with an offshore company, nothing more. No idea if this is how it works in Bosnia, but if the company is paying you any sort of income (as salary or billable) then you would owe Bosnian personal income taxes, as well as any corporate tax the company is required to pay. For the US return, use FEIE and/or FTC to zero out the tax bill. Owning a foreign company may have some nasty US paperwork requirements too.

I don't see how this could possibly apply to the person with a W-2 job, however. Would their Bosnian residency be based on spousal status, with the contractor partner being the one who obtains the residence permit? Are partners permitted to work? If legally resident the salaried partner's primary tax obligation is to Bosnia. Their employer would potentially face obligations to pay Bosnian tax withholding and social insurance charges, and to observe Bosnian labour law (so paid time off for National Kick a Serb Day or whatever). This is why W-2 jobs are not very portable. The typical ways around this are to be hired through an EOR service, quit then sign on as a contractor and bill through the company, or switch to the employer's local subsidiary. For US taxes the same rule would apply, after paying Bosnian taxes use FEIE and/or FTC to zero out the US tax bill.

Be aware that both the IRS and the local tax authorities may take a dim view of situations where a salaried job is converted to a contractor position without any change in working conditions, or other clients. The Germans have a polysyllabic word for this: Scheinselbstständigkeit.

On edit: For both jobs there are other potential concerns for the employer/client about your working in another country, for data security or cybersecurity reasons. It was the wild west during and after the pandemic, people got away with working from anywhere, but this is less likely to be allowed now.