The King of Far Far Away has died and Shrek and Fiona are to become King & Queen. However, Shrek wants to return to his cozy swamp and live in peace and quiet, so when he finds out there is another heir to the throne, they set off to bring him back to rule the kingdom.
This movie contains 19 potentially triggering events.
No, but there is a "generational trauma" plotline of Shrek being afraid he'll become an abuser because he was abused. He doesn't become the abuser this film (he does in Shrek Forever After but in a timeline that gets retconned).
Doris is a transphobic caricature. Women play stereotypical damsel in distress roles early on, but they learn to stand up for themselves and use their skills to escape being held prisoner.
There's a scene where Puss in Boots, who is established as a bit of a casanova, says to a cat that "she is his true love", only to be visited by a bunch of other cats that he also calls his "true loves". Another cat walks up to him and he tells her that he doesn't know her but he would like to in a flirty tone. The other cats then meow angrily and he runs away in fear. This is played for laughs.
A young man/teen is referred to as a girl (I'm not sure whether it's a legitimate mistake or not). What's worse is that it's played for laughs that one of the princesses, Doris, looks and sounds like she was born biologically male; she's even known as one of the "ugly stepsisters" in-universe. At one point, when she's attracted to a guy and says something like "He makes me hot!", one of the other princesses reacts with an "Eeeew!"
Shrek is referred to as "the fat one" in one scene. It's not really a joke, and Shrek doesn't seem to mind, but if the same thing happened to a person in real life, they'd most likely feel insulted/hurt.