Republican hard-liners in Texas thought this year’s primary elections would be the moment when, after years of trying, they would finally be able to take decisive control of the State Legislature.

They fell just short.

Though more than a dozen Republican incumbents fell to more conservative challengers, the party’s old guard rallied to protect the Texas House speaker, Dade Phelan, from being toppled by an activist endorsed by former President Donald J. Trump.

That victory in a runoff on…