When Billie Eilish first got famous, a rumor made the rounds that she was a record industry plant, a prefab teenage dream concocted in a lab somewhere by label executives and Eilish’s well-connected parents.

Similar charges have been leveled at everyone from Avril Lavigne to the Beatles, but in Eilish’s case it seemed particularly improbable. Her tendency toward whispery, ASMR vocals and often hook-less songs; her fondness for green hair and Ali G track suits accessorized with the oversized ’70s sunglasses of somebody’s Palm Beach nana. Who would have invented her?

It’s been years since fans worried much about pop stars being authentic — everyone just assumed they weren’t — but the unforced, Everygirl elements of Eilish’s origin story are foundational to her appeal. She recorded her full-length debut, 2019’s “When We All Fall Asleep, Where Do We Go?” in a bedroom studio in her childhood home, with her brother Finneas O’Connell as practically her sole collaborator. It went multi-multi-platinum, won six Grammys (including Album of the Year), and made Eilish the biggest phenom of her generation.

The second album is usually the hardest, but for Eilish, whose excellent sophomore release, “Happier Than Ever,” dropped on Friday, it’s particularly tricky: She must deliver an album that resembles her first one but is somehow different, that retains but also expands upon its bedroom intimacy. She must also bridge the invisible gulf that has sprung up between her and her audience.

Eilish now has the kind of all-encompassing superstardom that fans often find hard to forgive, especially in those who could ostensibly be their peers. She was them, and now she’s Them, a celebrity with stalkers (“Too bad they’re usually deranged,” she sighs on one track), residing in a secret house she bought, which she needs because she’s too famous to go outside. All her hookups have to sign NDAs.

There’s still more that unites Eilish and her young fan base than separates them, and “Happier Than Ever” meets any divide head on. It’s an album about feeling imprisoned — by your body, by expectations, by trauma, by the unrelenting gaze of others. Celebrity, like young adulthood, is awkward and exposing and destabilizing. In an era of selfies and TikTok, where everyone is micro-famous anyway, you don’t have to be a pop star to understand.

There’s nothing on “Happier Than Ever” that makes it feel dramatically different from its predecessor, though it’s in almost every way improved. The arrangements are more deft and the songwriting more assured, even if it doesn’t always hit as hard. It was crafted in much the same way, in her brother’s home studio, with O’Connell again serving as producer and co-writer. These songs remain defiantly internal in every sense, reminders of what an outlier Eilish is, and the scant interest she has in the signifiers of a hit album in 2021: the army of outside co-writers, the Jack Antonoff-produced tracks, the never-quite-natural guest features.

On the opening ballad, “Getting Older,” her teenage angst has paid off well, and now she’s bored and old, or at least it feels like it to her: “I’m getting older/ I think I’m aging well,” sings Eilish, at 19, with no more apparent irony than usual. “Things I once enjoyed/ Just keep me employed now.”

“Happier Than Ever” is a confident, somehow cohesive mix of whisper ballads, electro pop tracks and several songs that feel like standards, with arrangements that veer close to jazz, such as the leisurely first single “My Future,” or the coo-ey “Halley’s Comet,” one of several tracks likely influenced by ’50s torch singer Julie London. On the undercover romance ode “Billie Bossa Nova,” Eilish alternates between sounding tentatively flirty and surprised at herself, a push-pull that becomes one of the album’s recurring themes.

Things occasionally flag. There are too many ballads that lack any animating force, that seem lifeless instead of languid. The whisper-spoken tone poem “Not My Responsibility” (“If I wear what is comfortable/ I am not a woman/ If I shed the layers/ I’m a slut”) is a slog.

The more clattery things get, the better. “GOLDWING” and “NDA” are appealingly twitchy club tracks; the former begins life as choral hymn, the latter suggests one of Eilish/O’Connell’s many homages to midcareer Nine Inch Nails. The title track, initially a standard issue, sluggishly tempoed Eilish ballad, shapeshifts halfway through into a monster wall of distortion aimed at her drunken-driving, perpetually late and generally problematic older boyfriend. It may be her greatest moment.

“For anybody asking, I promise I’ll be fine,” Eilish sings on “Getting Older.” There’s been no reason to doubt her yet, but “Happier Than Ever” can’t help but feel transitional, a liminal space between the aggrieved, phantasmagoric teen melodrama of her debut and whatever bright thing comes next.