How would interstate water compacts be handled after independence?

They convert from agreements between states into agreements between countries, and the water keeps being divided on the same terms. This is a change of legal category, not a change of substance, and it is exactly how neighboring nations share water everywhere in the world.

What an interstate compact is

A compact is a negotiated agreement, approved by the legislatures involved, that divides a shared resource between states. For water, it sets how much of a shared river each state may use. Texas is already party to a full set of them: the Rio Grande Compact, the Pecos River Compact, the Canadian River Compact, the Red River Compact, and the Sabine River Compact. These agreements already do the hard work of dividing shared water, and they already function without Texas owning any of the rivers outright.

Independence reclassifies them, it does not erase them

When Texas becomes independent, a compact between Texas and another American state becomes an agreement between Texas and a foreign country. The allocations can carry forward unchanged. What changes is the heading on the document and the body that enforces it, which moves from the framework for interstate disputes to ordinary international practice. Nations that share rivers, and there are many, manage them with exactly this kind of bilateral or multilateral agreement.

Existing terms are the natural starting point

There is no reason for either side to tear up a working allocation. The farms, cities, and power plants that depend on a shared river need predictability above almost everything else. The sensible path, and the one that protects everyone who relies on the water, is to carry the existing division of water into the new agreements and adjust only by mutual consent over time, the way water agreements have always been revised.

Texas negotiates for itself

The upgrade for Texas is representation. Inside the union, shared-water arrangements that reach above the state level involve the federal government on Texas's behalf. As an independent nation, Texas negotiates and enforces its own water agreements directly with its neighbors. The state with the most at stake in Texas water gains a direct hand in protecting it.

The bottom line

Interstate water compacts become international water agreements. The allocations carry over, the water keeps flowing on the same terms, and Texas represents itself at the table for the first time. The category changes. The water does not.