Just Got Notified Of 2 Speeding Tickets From 1993 And 1997, Filed Today. What Are My Legal Responsibilities?

Basically, the title.

I pay Experian to watch my credit and identity. My credit file is locked.

I got a notification that new court records were filed Today. It says a speeding ticket from 1993 and 1997.

Is this legal? e.g. Statute of Limitations.
Do I have any legal responsibilities regarding these two speeding tickets?
Should I be worried that I might have warrants out for my arrest? The notification says that they were "Guilty" and "nolo contendere" or No Contest.

I have very blurry memories from +-30 years ago. I know I got pulled over and ticketed in that county around that time, but I have absolutely no memory of the outcome of those tickets. Moreover, I know I had a ticket that was never filed around that time, but I do not remember in what county or city or anything else about it.

Does the statute of limitations hold up after 27/31 years for speeding tickets?

Texas, United States.
I lived in Texas then, and live in Texas now. I have never lived in the city/county where this took place, but have driven through plenty.

Please help me figure this out and if I might be responsible for these tickets ~30 years later, or if it's just getting filed and there's nothing I need to do.