How is Yaku's life more embarrassing than Yani's, who's a bacteriologically unsafe slob living in complete filth, or Aru, who's a barely sentient alcoholic wreck...
This is actually an incredibly deep question.
Hame, being a streamer, is obsessed with public optics and appearances because she's a content creator who wants to curate a public image of herself. Her eating the bug on stream was probably more psychologically damaging to her than Yaku making her wet herself.
Content creators, at least all of them that I've known in life, are constantly on guard against doing something embarassing on stream, unless making an ass of yourself on stream IS your brand.
A stray comment can become your undoing with chat in seconds. Chat also reminds the content creator of every fuckup they've ever done on stream constantly. Streamers always have a demon on their shoulder telling them they've fucked up and they're an embarassment. Hame, I'd imagine, is no different. She probably feels like she's cringe as fuck all the time because she imagines what chat would say to everything that happens to her on and off stream.
To that end, Yani and Aru's lives, pathetic as they are, are private. The general public Hame interacts with online doesn't know about them other than what she's tried to expolit by putting them on her streams. If Yani or Aru really wanted to, they could still curate a public image and chat wouldn't know the true depths of their problems.
Yaku, on the other hand, wears a scarlet letter in life. Yaku's public image is one of shame and embarassment by order of the state. To Hame, that means that Yaku can never curate a public image like her without chat already knowing her darkest secret, something Hame is on guard against all the time.
That's what Hame means by having a life more embarassing than hers. That at least Hame doesn't have a public mark of a criminal for chat to use against her.