Here’s the whole section you’re selectively quoting

How does party affiliation work in Texas? In Texas, there are several main ways for a voter to affiliate with a party: by being accepted to vote in a party’s primary election, by taking the required oath at a party precinct convention, or by taking a party oath of affiliation generally (§§162.003, 162.006, 162.007). A voter’s affiliation with a party automatically expires at the end of each calendar year, which is December 31. (§162.010). A voter who has affiliated themselves with a party is ineligible to participate in the party affairs of another party during the same calendar year. (§§162.012, 162.013)

Emphasis added to show that there is no persistent, year-over-year affiliation (I emphasize this word because there is no party registration in Texas)

And the only way you can vote in a primary is to register with them

I have never registered with a party. There is no field for party affiliation in the online voter registration form

https://vrapp.sos.state.tx.us/index.asp

And the registration certificate doesn’t include a party affiliation

https://www.votetexas.gov/register-to-vote/voter-registration-certificate.html

And a Non-potato quality picture

https://disabilityrightstx.org/en/handout/understanding-your-texas-voter-registration-certificate/

you can do it on the spot if you want, but once you do it, that’s it

Every primary election I’ve participated in the official who checks you in just asked which primary you want to vote in. And since voter registration in Texas does not track party affiliation you’re going to have a rough time convincing me this counts as registering with the party.

The spam you’re getting is simply because it’s public record whether you voted in any election, including which primary you voted in. But it’s not the same as other states recording your party affiliation as part of your voter registration, which Texas flat out does not do.