Imagine some preindustrial scientist being awakened in the modern era to find that the aether has been first debunked for more than a century and then rediscovered, but with different rules.
(Well, that's only true if you assume there's no as-yet undiscovered fields and particles with FTL that we could eventually interact with -- then we would be able to get something like measurements of speeds of everyday particles and photons relative to such fields, and if they were much faster than light then those measurements would look like "absolute speed" to us. But that's sci-fi fantasy.)
Higgs is not aether for electromagnetic waves. It's only a wee bit like aether for matter if you squint real hard, but still, it's not a medium of travel for matter, so it's not an aether.