A travel eSIM is always roaming, by definition: it is a foreign line using a local network. Data roaming has to be on for it or nothing works.
iPhone: Settings → Cellular → tap the travel line → Data Roaming on.
Android: Settings → Network & internet → SIMs → tap the travel eSIM → Roaming on.
Your home line is the opposite case. Leave data roaming off there, so your own carrier is not selling you data you have already bought.