General Discussion

I think that the system allows the voter to choose, in this case, among the 5 top candidates in the two primaries.

If a Republican is voting strategically, he or she would vote for Cornyn, as Paxton weakens the Republican chances.

I would agree with you if Cornyn was running for reelection unopposed, then the perceived weaker Dem candidate may be considered. But in this case, a Republican voter looking forward to the General Election needs to knock out Paxton.

I also think you overlook the double digit unfavorable for Trump. As a result, those Dem voters are looking to flip this state.

There are 4 choices for a voter, as I see it. If you are a MAGA Republican, you're taking a Republican ballot and voting for Paxton. You're not risking voting in the Democratic primary for someone you don't like, while your kindred spirit in in a close fight on your own side. If you're a moderate Republican looking to save the Senate seat, you're voting for Cornyn. If you're a moderate Republican or Moderate Democrat who wants to send Trump a message, you're voting for Talarico. If you're a Progressive Democrat and want to send Trump and the Dem leadership a message, Crocket is your candidate. I don't see crossing over for strategic reasons when there are such diverse choices in very close elections