Looks like eBird/Clements call Larus canus ssp. canus "Mew Gull (European)"

Yes, Larus canus is typically called Common Gull in Europe, but Mew Gull is hardly a Clements-exclusive name: IOC, HBW/BirdLife, and H&M all use Mew Gull for L. canus sensu lato (and HBW goes so far as to give the name Mew Gull, not Common Gull, to the nominate subspecies as well!). In any case, this isn't as clear-cut an example of "America vs. the rest of the world" as you make it out to be, and if either name could be considered "globally accepted" for L. canus s. l., it's probably not Common Gull.

I'd also argue that, with a few exceptions (e.g. if the taxa are completely allopatric and one has a much smaller range than the other, or in a small number of cases like the Circus cyaneus or Lanius excubitor splits where a different name was already in use for each post-split taxon, which could potentially apply here, but see above), in the event of a split, it's usually best if a pre-split common name isn't used for any of the post-split species. Sure, having to get used to a new common name for your local birds can be a bit confusing at first, but retaining a common name for some, but not all, populations of the birds it once referred to can cause its own host of problems (like continued erroneous reporting of the wrong taxon in an area far into the future by birders unaware that the split occurred - see e.g. retention of the name Winter Wren for eastern North American birds). In the present case, each of the potential splits has its own perfectly good common name, separate from the collective Mew Gull: Common Gull for canus (including heinei), Kamchatka Gull for kamtschatschensis, and Short-billed Gull for brachyrhynchus.

(And as for the three small Stercorarius, IOC and HBW/BirdLife call those jaegers too [and that's not an American-specific term, either - jaeger is in common usage in Australia, too].)