An entity can't be a subsidiary and a branch at the same time ...
A foreign-owned single-member LLC that doesn't elect to be taxed as a corporation is a disregarded entity, it doesn't matter if it's owned by a physical or legal person.
If an LLC is considered non-ETBUS, it's not taxed in the US at all, period, because it doesn't derive it's profit from the US. It's place of business, it's permanent establishment, and place of effective management are elsewhere. It only has a registered address in the US, that's all. It is most likely taxable in the place where you actually do the work, or do the management.
The Polish IP box is a good idea. Also good idea is a
Romanian micro-company. Revenue tax is only 3% or 1% if you hire someone (min wage in
Romania is 466 EUR). Social charges and healthcare are absolutely minimal and capped. As a single person, an US LLC is in fact not a good idea, because if you run it from some other country it'll be considered there as a branch of the LLC, taxed with a full CIT, losing rights to any preferential treatment as a domestic company would, like in case of Romania the LLC wouldn't be eligible for the 3% / 1% tax rate, it'd pay the full 16%.
In the worst case it'd be recognized as tax-transparent and you'd have it all taxed as your personal income.
With a Romanian company you can take advantage of the relaxation of
CFC rules within the EU. If you create an economic substance in Romania for the company (rent office, hire someone ...), you can live anywhere in the EU and the local tax authorities can't appropriate it for taxation, it will remain Romanian with the 3% / 1% tax rate.
Moreover if you need to provide somewhere a
company registration record from a public register, or board meeting minutes, anything that a normal limited company has, for example for opening a branch office, with an US LLC you cannot, because none of this exists.
You cannot hide with it anymore because foreign ownership is being reported to the IRS, and the IRS passes it on to your local tax authorities, along with the LLCs financial information for taxation.
I own an US LLC and after learning about all these legal rules, it seems a bit pointless to have, even disadvantageous sometimes.