influence, inevitable due to their major labels and marketing, media presence, etc etc. good pop songs. influence on the cultural mores/social justice warrior concerns of millenials (eg feminism, LGBT rights, etc etc).
I just don't see where Gaga's influence is? Her politics have been very very flimsy and outdated. Beyonce's last 3-4 years have had more adherence to so-called SJW mores than Gaga, who kind of has no further lip service to anyone than say Madonna might've. Madge's was just more implied than how Gaga explicitly made hers about (both also get proven to be more and more crass with time).
Also Gaga isn't so much a creature of Marketing as much as she's an active participant of the industry who the industry rewarded; she was ghostwriting or regular writing, and then came up, and that became a very very frequently rewarded model within the last decade or so in pop (Ke$ha) or genres not considered inherently mainstream (Frank Ocean, PartyNextDoor). She wasn't say a Britney Spears who learned how to be a pop star through self-development and training to be a dance/vocal entity. She was actually originally a singer-songwriter in the Regina Spektor vein who slowly tried to work her way in (Kesha, another parallel I keep going back to, was the daughter of a music industry pro).
If anything, were other people who followed in her footsteps AWARE of that as a career model, that would be her influence for sure. But very very few people as artists were as impacted by her as you think. Of course, maybe that's because her absolute irrelevance for the past 3-4 years has made it feel that way, especially how she tried to latch onto Beyonce (the definite everlasting popstar of the last two decades give or take) and instead got chewed up and spat out. Hell Beyonce even got the better duet.