Why does data roaming need to be on?
Because that is how a travel eSIM connects. It uses partner networks in the country you visit, and your phone labels any partner network as roaming. Turning Data Roaming on for the eSIM line is required, and it does not cost extra. Your plan is prepaid.
Roaming on the eSIM is not roaming on your home SIM
The scary roaming bills people remember come from home carriers. That risk lives on your home SIM's line, not on the eSIM.
Keep data roaming off on your home SIM and on for the eSIM. Then nothing can bill you by surprise.
Where the setting lives
On iPhone: Settings, Cellular, tap the eSIM line, turn on Data Roaming.
On Android: Settings, Network & Internet, SIMs, tap the eSIM, turn on Roaming.