Do you need sea water of just salt water equivalence? Sea water is about 3.5% salt. It might be worth trying to use bleach solution and dissolve salt in that.

Refresher of calculations:

https://courses.lumenlearning.com/cheminter/chapter/calculating-ph-of-salt-solutions/

Better to use the seawater separately and then distilled water which you can then adjust the pH to your desired value...But, if you insist on adjusting the seawater pH to 12, you may try KOH instead of NaOH and observe what happens....If precipitation occurs again, continue to adjust the pH to 12 and then filter the seawater afterwards..

Now a days the CO2 emission is increasing resulting, Ocean acidification is a powerful reason, in addition to that of climate change, for reducing global CO2 emissions. The major carbon reservoir in the ocean is in the dissolved inorganic carbon, which is the total of aqueous CO2, bicarbonate (HCO3) and carbonate (CO3) ions. The pH of seawater is dependent on which of these species is the most predominant. The normal present day pH of seawater is more on the basic side between 7,9 – 9,0. At this pH the HCO3 ions predominate.Buffer capacity will change with a temperature increase because CO2 concentration will decrease (according to Henry's law) and so bicarbonate concentration will also decrease (Le Chatelier principle) according this reaction: 2 HCO3- + Ca2+ -> CaCO3(s) + H2O +CO2 (degasing).NaOH and KOH are the CO2 absorbent and KOH solution absorbed CO2 more than NaOH.

Coloque el agua de mar en un baño de maría con hielo para mantener el agua fría y agregue lentamente NaOH hasta que alcance el PH 12.

pH is a determined value based on a defined scale, similar to temperature. This means that the pH of water is not a physical parameter that can be measured as a concentration or in a quantity. If the pH of water is too high or too low, the aquatic organisms living within it will die. pH can also affect the solubility and toxicity of chemicals and heavy metals in the water. The majority of aquatic creatures prefer a pH range of 6.5-9.0, though some can live in water with pH levels outside of this range. Spread across the world are many lakes with unusual pH levels. Alkaline lakes, also known as soda lakes, generally have a pH level between 9 and 12. This is often due to a high salt content (though not every salt lake has a high pH). These lakes have high concentrations of minerals, particularly dissolved salts: sodium, calcium, magnesium carbonates and bicarbonates. Depending on the lake, borates, sulfates and other elements (usually strong base ions) can also be present. Alkaline lakes are formed when the only outlet for water is evaporation, leaving the minerals behind to accumulate.

* https://www.fondriest.com/environmental-measurements/parameters/water-quality/ph/ Saja Mohsen

Esto lo afirmo porque el PH del agua de mar ( 7>PH>8.7) disminuye su PH al aumentar la temperatura, esto es a escala de laboratorio, no para un lago donde el PH cambia dependiendo de la profundidad.

You can increase the pH by adding calculated amounts of Calcium Carbonate, Magnesium Carbonate and/ or Magnesium Chloride.

Why not synthesis

Use alkaline solution..