I play on a multiplayer server with one other individual, and we have defeated the end dragon together 4 times, and have not had an end gateway spawn for the outer islands at any point. We have tried reloading the end, relogging, and updating the server to the latest snapshot (20w29a), all of which have failed to spawn an end gateway after killing the dragon.
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Yes, though we did not defeat the dragon or enter the end until after we had updated to 1.16.1

Please read the moderator note on MC-184482, and in the future, please be more vigilant when using early development builds.
Did you open the world in 20w20b, 20w21a or 20w22a?