Supergirl is fine. I don't know if they know what they want to do with most of these characters, though. Kara seemingly has no character arc, and she doesn't seem to learn anything or grow at all. Is she attracted to Lena? Is William supposed to be a romantic lead? I honestly have no idea what her character really is. I think the writers seem to have a lot more fun with J'onn and Nia and Brainy and Alex. Kara's really just there to do the fight scenes and go back and forth to check on how the characters are doing. Am I wrong here?
I've enjoyed Melissa Benoist in every season of SUPERGIRL. I don't take any issue with her character in Season 5, but I don't disagree that she lacks an arc in Season 5. I'm not sure she needs one right now. The main thoroughline of Kara in Season 5 is that she has merged the two halves of her life, or she at thinks she has. From a plotting perspective, it makes sense to give her an 'arcless' period of stability before Lena overtly turns on her or Kara discovers that Lena considers her a treacherous enemy.
That said, I'm trying to be more open to different kinds of characterization. In Season 1, the writing for Kara Danvers was a mess: she was an entry-level intern at a news agency who was a top level secret agent employed by a government espionage agency who was struggling to keep a secret identity amidst a regular cast where everyone except Cat Grant knew all about it who had a close relationship with Superman although Superman never appeared in person.
Season 2 got its act together at last: Supergirl is the friendly superhero face of a covert spy agency; Kara Danvers is a nervous mess of a human being who has to get her act together when trying to mentor a shiftless layabout, Mon-El, in the superhero game. Supergirl was everything Kara could never be in civilian life.
Season 3, unfortunately, got confused again and this was a season where Kara's only real arc was her grief at Mon-El returning a married man. There was a lot of intrigue over Kara's Kryptonian heritage, but Kara didn't really have a strong direction this season, likely because sexual harasser Andrew Kreisberg was fired off the show halfway into the season and none of the writers wanted to use his planned material once they were rid of him.
Season 4 was good, exploring how Lena is Kara's most rewarding relationship and Lena can't stand Supergirl. The constant collisions between Kara's civilian and superhero life were played out beautifully as Kara discovers that Catco's reporting is at threat, as Supergirl finds that she's part of a discriminated minority, as Kara finds that the ordinary people she lived among for most of her life consider her the other, as Supergirl realizes that she's part of a government agency that is falling entirely in line with a xenophobic White House administration.
The most heartbreaking moment of Season 4 was when Alex is forced to have J'onn erase Alex's memories of Supergirl and Kara feels truly lost. There's another beautiful moment where Supergirl, unable to defeat a Kryptonite fuelled villain and in a jail full of people who hate her, switches to Kara Danvers and is astonished to be dismissed by Supergirl's attacker and embraced by an inmate who is a devoted reader of Kara's articles. And the season finale is where Kara and Supergirl are at last united: Kara exposes the President and Supergirl stops Agent Liberty. Season 5's premiere was, to Kara, the seeming conclusion to this storyline where she tells Lena who she really is and now we're dreading how Kara thinks all is well when she has no idea what she doesn't know.
... is Kara in love with Lena? I think Kara and Lena should be the romance of the show -- but I don't think it's going to happen. I don't think it was planned for Katie McGrath to have such chemistry with Melissa Benoist, but it happened and the writers have tried to steer into it as much as they can, they've made the Kara/Lena friendship the center of Season 5.
However, Supergirl is owned by a corporation that took over seven decades to concede that Wonder Woman is bisexual (and that's with Wonder Woman living on an island nation of immortal women and no men since 1942). The character of Supergirl as she's been portrayed since 1959 is a boy crazy teenaged girl; letting the Melissa Benoist Supergirl be bisexual implies that every version of the character is the same because Benoist is the most commonly known rendition. I don't see this slow, lumbering and heteronormative multinational finding the institutional will to make one of their iconic properties bisexual based on the specific chemistry between one performer playing the role with a specific scene partner.
That said, accidents happen and good shows capitalize on them. ARROW realized that, despite Black Canary and Green Arrow being a couple in the source material, the onscreen chemistry of Stephen Amell and Emily Bett Rickards was the way to go whereas Katie Cassidy was better as Stephen Amell's friend. COMMUNITY planned for Troy and Pierce to be best friends; they soon realized the real bromance was between Donald Glover and Danny Pudi, just as they realized that Joel McHale's best scene partner was not Gillian Jacobs but Alison Brie. SUPERGIRL realized that Winn, despite being a Catco employee, worked better in the spyfi environment of the DEO and made the change for Season 2. MACGYVER started out with MacGyver a gunslinging, arrogant action hero but realized the actor was better as an unarmed innocent. SLIDERS meant for Quinn Mallory to be an unathletic, socially inept geek, but Jerry O'Connell transformed the character into a damaged, self-isolating athlete brainaic and Tracy Torme ran with it.
I doubt SUPERGIRL will capitalize on Supercorp any more than it's chosen to; SUPERGIRL has made Lena the most passionate friendship in Kara's life and I think that's all it can be. Institutionally. If SUPERGIRL were an original property and the showrunners could make decisions without worrying about whether or not they can use the Suicide Squad or get their content past DC Comics, I do think Kara would have been out and proud by the middle of Season 4.