From my research on embedded SIM (eSIM) technology, it's a SIM card that the consumer owns and is capable of downloading and switching between 3rd party subscriptions. I've also read it's expected that most eSIMs will run a Java Runtime and support Java applets [1].
Is it possible to program Java applets onto eSIMs, similar to programming a Java smart card?
[1] "EUICC45", https://www.gsma.com/newsroom/wp-content/uploads/SGP.21_v2.1.pdf
Yes. The active specification.
2.4.11.1 Java Card packages An eUICC supporting Java CardTM SHALL support the Java Packages listed below. The implementation of each Package SHALL as a minimum be according to the given Package version and Specification version
Then a list of the supported packages