It is two fundamentally different abilities. Haki is a spiritual ability, an invisible armor to coat yourself in.
Tekkai is something entirely else - hardening the user's muscles and it prevents the users from moving which has never been the case with Armament haki users... It is two different things which achieve a similar result but different nonetheless.
Exactly.
Jabra also only used it in moves, where his posture stayed static, he just had to initiate them with a certain amount of momentum. He wasn't really "freely" moving around.
Blueno did it the same way with a tekkai based superman fist, that he initiated with the momentum from Geppou.
That movement restriction aspect totally makes no sense for a CoA retcon, especially cause like all the other moves, except for Rokougan, it's totally explainable w/o haki.
Paper cut might feature CoO, but that's just really that.