How does anyone know if it's permitted or not? Does the city make it public knowledge?

Not sure how OP is verifying, but to answer your other question, the city has a page for public information (budgets, maps, schools, etc) that includes a data set of all permits issued going back several decades https://data.cstx.gov/

Thank you for reporting this concern. Code Enforcement will investigate whether the property in question is in violation, and take appropriate action. Updates will be posted here. Please contact Code Enforcement at 979-764-6363 or at str@cstx.gov for any questions or concerns.

Agreed that the city has pages for various public data, but I'm not sure either how OP is substantiating the "offense". Everything I've found relative to this has a charge: if someone's paying to play Karen or mall cop, that's sad.

Here’s a map of all STR’s https://cstx.maps.arcgis.com/apps/instant/basic/index.html?appid=bab6512ee20340149e1a2070430cba2d