A couple of bits here..
The first has already been mentioned - enabling the roaming facility is an account-level function, not a phone menu setting which I suspect you're confused with, You're not the first, and won't be the last, to think that "data roaming" (or similar) menu options are the place to check.. unless you checked with EE-CS, or texted ROAMING to 150 before leaving the UK... then your SIM doesn't have permissions to connect to foreign networks. That causes a lack of coverage abroad, and the rest of your symptoms are the natural consequence.
More importantly, you mention about deleting your eSIM... that will very likely do for you being able to roam now. Even without enabling roaming before leaving the UK, you could have contacted EE-CS using another working phone or web-calling app and resolved by requesting roaming was enabled.
By deleting your SIM, you will now need to have a new SIM activated before you can enable roaming in-turn. A replacement physical SIM can only be posted to your UK address, while any new SIM (be it physical or electronic) usually requires activation on EE's UK network before roaming can be enabled. There is an outside chance that you can get a new eSIM activated whilst abroad, but trying to do the activation & roaming enablement - whilst already abroad - comes with plenty of risk and no guarantee.
Be prepared to not be able to resolve this until your return to the UK.
