Your concern is well-founded. You need to be affiliated to the statutory healthcare system in another EU member state to be covered by the EHIC system. CitizenshipThis means that citizenship as such is irrelevant, you really need to reside in the EU (even if you're not an EU citizen).
That also means that it will still be possible for British citizens to get a EHIC, provided they reside in the EU (whether under the transition regime from the withdrawal agreement or as a third-country national outside of EU law).