I have used Airalo, but the downloaded Esim if for the phone not the watch.
Your watch will not work on cellular unless your carrier supports international roaming.
Airalo does not support this for a watch.
International roaming with your Apple Watch
With watchOS 9.1 and later, international roaming is available on cellular
models of Apple Watch Series 5 and later, Apple Watch SE and later, and
Apple Watch Ultra.
To get
international roaming on your Apple Watch, contact your iPhone carrier
to add your watch to your iPhone cellular roaming plan. For
international roaming to work on your Apple Watch, your carrier must
support VoLTE and roaming. Not all carriers support international
roaming on Apple Watch and coverage in other countries is determined by
your carrier.
To turn on international roaming, open the Settings app on your Apple Watch. Tap Cellular, then turn on Data Roaming.
International roaming isn't supported on cellular models of Apple Watch that were set up using Apple Watch For Your Kids.
To cover the LTE and UMTS bands used around the world, cellular models of
Apple Watch come in regional models for the Americas, China mainland,
and Europe/Asia Pacific. Unlike iPhone, there isn't a worldwide Apple
Watch model that supports all cellular bands used globally. Find out which carriers in your country or region offer cellular service for Apple Watch.