Also wonder if that calibration solution settles in the bottle and can change the reading?
No. Calibration standards neither go bad (except by evaporation) nor ever settle.
In fact, no dissolved chemical can ever settle out of (or rise to the top of) water. The thermal motion alone is enough to keep water solutions homogeneous.
Some refractometers are designed properly for seawater and are always called true seawater refractometers. If those are made perfectly, remain perfect, and are calibrated perfectly, then RO/DI is adequate.
Many hobby refractometers are not designed for seawater, but are repurposed brine refractometers. No matter what the instructions say, if they are made perfectly, remain perfect, and are perfectly calibrated with RO/DI, then will be inaccurate for seawater for well understood reasons (in short, the refractive index vs salinity profile for brine is different than for seawater).
In both cases, and whether it was made perfectly or not, and regardless of whether it remains perfect, calibration with an accurate 35 ppt standard will always give the right salinity at or near 35 ppt.