Squidward

What he usually thinks about
About silence and peace. He is constantly irritated by the noise and frantic energy of SpongeBob and Patrick. In his head, he often thinks something like: "When will they finally settle down?"
About his creative side. Squidward considers himself an artist: he plays the clarinet, paints, and dreams of recognition and the big stage. His thoughts are full of hopes for success, but almost always mixed with disappointment that his talent seems to be appreciated by no one.
About the job he absolutely hates. He is a cashier at the Krusty Krab, and this job feels humiliating and boring to him. In his mind, he often contrasts it with his high artistic aspirations.
About his neighbors. SpongeBob sincerely considers Squidward a friend, but Squidward himself perceives him more as a source of endless problems. His thoughts about SpongeBob are a mixture of irritation and (sometimes, almost imperceptibly) a quiet affection.
About self-respect and status. It is important for him to seem sophisticated and "above" the mundane hustle and bustle. He often thinks about how to emphasize his exceptionalism and separate himself from "ordinariness."
How this manifests in his lines
In the series, his inner world is clearly read through his phrases: he sighs, sneers, or dreams out loud. For example, his sarcasm and tired comments are exactly his thoughts voiced: "I can't take this anymore...", "This is simply unbearable...", "I am an artist, I deserve more!".

Dissatisfaction with his surroundings. His biggest pet peeve is his noisy and carefree neighbors, SpongeBob and Patrick. Squidward finds their behavior frivolous and annoying, though they don't even realize it and sincerely consider him a friend.

Job aversion. He works as a cashier at the Krusty Krab, but he loathes the job. He's irritated by both his greedy employer, Mr. Krabs, and the very need to constantly interact with SpongeBob.

Dreams of a different life. Squidward dreams of something bigger: becoming a famous musician or artist, getting rich, realizing his creative potential (he plays the clarinet and draws). But he usually fails to realize these dreams.

Feeling misunderstood. He often feels undervalued: others don't see his talents, yet he's unable to honestly acknowledge his own shortcomings. He tends to blame the outside world and other people for his failures.

Internal contradictions. The paradox is that, despite his grumpiness and even bitterness, Squidward sometimes wonders: what if life really would become empty and boring without these noisy neighbors?