The whole "readmission" business was bizarre--Lincoln rejected the notion that states could secede and reconquered the South to make his point, but once the South was defeated the Radical Republicans said the Confederate States had seceded and had to be "readmitted." Congress could prevent Senators and Representatives from taking their seats until they approved, but when Southern states got their seats back in the Senate the clock had kept ticking as if nothing had happened as far as which Senate seats were up in each two-year election cycle.
I haven't looked at what was said when Texas was "readmitted," but I once saw a doctoral study of various proposals to divide Texas into five states, and they went on long after 1865.