To add to Xray's reply, I'll pick up a couple of misconceptions here. Your post opens up several issues, so this reply is necessarily long.
When you are roaming, you use the radio coverage of the local network in your host country, but your data traffic is still usually routed through EE's core network in the UK.
Equally using an E-SIM in China is not the important bit, rather it's who issued the SIM. If it was a Chinese network, then your data is routed through them. Travel SIM providers would have their own arrangements for handling data traffic and deciding on routing, but the fact it's an electronic rather than physical SIM is immaterial in this regard. This is exampled by EE routing data exactly the same regardless of whether you have an eSIM or a pSIM.
As mentioned above, the roaming pass is just a means to mitigate the cost of using your phone abroad. It has zero bearing on the routing of your calls, text & data traffic - its only impact is on how your usage is charged for once the billing records pass through EE's systems in the UK.
All this said, EE is a UK operator and its roaming services are intended for users making short trips abroad - not for those long-term resident outside the UK. This is broadly enforced via the Stable Links policy, which generally requires usage in the UK for 2 months in every 4. If you can't meet this criteria due to long-term residence outside the UK, then you need to consider one of two options.
1: Be prepared to pay full roaming rates sooner-or-later and roam whilst maintaining your monthly contract.
2: Consider migrating from pay-monthly to PAYG in plenty of time to complete this before travelling, and accept the cost of early termination.
Migrations from pay-monthly to PAYG require 30days notice, and every new PAYG SIM needs to be used in the UK first, before roaming is auto-enabled for use abroad.
In anycase, PAYG lines are subject to the hibernation policy which requires chargeable usage at least once every 179 days to avoid suspension.
