As a masters student in brand marketing, I've had SO MANY gripes with this roll-out. So, not like anyone asked, but this is what I would have done if I was in charge of her roll-out -

Step 1: Start up promo by doing as many YouTube collabs/magazine interviews as possible to hype up the upcoming start of a new era. (NOTE: This is the only part of her actual roll-out I feel was done well!)
Step 2: Release "Tonight" as the first buzz single long before the album release. Drop it alongside a video. Emphasize that the early 2010's sound as a conscious choice and use that as the marketing ploy. (Millennials have hit, or are inching towards their 30's and 2010's nostalgia will be easy to capitalize on. This push alone would lead the song to chart on the Billboard Hot 100, probably somewhere around 80-100. More importantly it would rope-in a lost percentage of her old "Animal/Cannibal" era fans who would go on to buy the album after being reminded of their high-school/college glory days.)
Step 3: Push the "Tonight Challenge" on TikTok. It would basically be people going comedically over-the-top, trying to hype-up their friends to the tone of "bitch we going out tonight!". It's lame af, but the younger demographic will eat it up, causing the single to gain in popularity, maaaaybe even hit top 40.
Step 4: Album pre-order goes up. "Shadow" included as pre-order bonus/first official single. Perform on late-night talkshows, and pray it sticks. Grind as hard as possible with promo to get the adult-contemporary demographic. Get the attention of those "oh she was great at the Grammy's!" fans. If done right, the song could easily hit top 20 with massive staying power thanks to radio play.
Step 5: Drop an uber-glamorous video for "Shadow" to purposely contrast the gritty "chick at a dive bar" era aesthetic. Inspire tons of "Kesha Shadow make-up look tutorial" videos to drive traffic from that demographic, and increase the singles staying power.
Step 6: Release "Resentment" and "Raising Hell" as a dual-single drop 2 weeks prior to album release. Give "Resentment" the promo budget. Serve it to country radio, pop radio, classic rock radio, everything. It would have stuck eventually. Perform it as much as possible live, meanwhile releasing an accompanying video for "Raising Hell" to feed the fans who aren't completely satisfied with the ballads. (It's a campy western theme video to capitalize on some of the Old Town Road "lol ye-haw" demographic.) (NOTE: The campy religious vibe of the actual video was a major mistake. It surely alienated some of the "Praying" fans she earned after the Grammy's performance.)
Step 7: Drop the album. Release "My Own Dance" video on album release day. Sweep it under the rug. It's pure fan service. Keep pushing whatever single has performed the best thus far.
Step 8: Release "Kinky" as the album's final "pushed" single 2 months after album release. Release a video with a bunch of popular drag queens. Guest judge on RuPaul's Drag Race, where they would use it as the elimination song for the episode. Pride performances. Show up to random gay bars and perform it live - reminiscent of Gaga's "Perfect Illusion" dive-bar promo tour. With the right promo, the could easily be one of those songs that lingers somewhere in the 40's on the Hot 100 for several weeks.

Thank you for coming to my Ted Talk.