It's improbable that for such a small-scale structure, they would start cross-border tax investigations, which is expensive.
You're probably right.
It's important to note that an additional benefit of operating as a branch office is that your identity will not be reported as UBO in this jurisdiction (or EU UBO register) since branch offices are exempt from UBO reporting, so consequently information about them shouldn't be reported between authorities as smoothly compared to companies.
That's a nice cherry on top.