Muggles saw some of the events but not all
"The Zouwu comes barrelling through the town and wrecks cars, then gets sucked down a suitcase."
Muggles almost certainly saw the Zouwu when Newt saved/captured it in his case. The incident takes place on a "Parisian Bridge" and people are said to have seen it including those in cars who must have certainly been Muggles.
SCENE 62
EXT. PARISIAN BRIDGE—NIGHT
In the middle of the bridge is the Zouwu, terrified and lethal. It is too badly hurt to keep running, but it is swiping at passersby, who are screaming and running out of the way. Cars screech to a halt.
Fantastic Beasts: The Crimes of Grindelwald - The Original Screenplay
Of course the Muggles don't see what happens when the Zouwu escapes initially as that occurred at "Place Cachee, Circus Arcanus" a place that is magically hidden from the Muggles.
SCENE 40
EXT. PARIS, PLACE CACHÉE—NIGHT
A clear, starry night. TINA GOLDSTEIN, reinstated Auror on a mission of her own, more elegant and confident than in New York but carrying private sadness, walks toward the bronzed statue of a robed woman set on a tall stone base, where witches and wizards dressed as Muggles are vanishing.
Fantastic Beasts: The Crimes of Grindelwald - The Original Screenplay
"Grindelwald’s big black capes swoop in and cover the whole city."
The Muggles cannot see the black banners that Grindelwald calls to summon his acolytes.
All lights are extinguished as every building is wrapped in black banners.
Muggles pass, totally immune, but a YOUNG RED-HAIRED WITCH nearby is walking along. She, like NEWT and TINA, can see the banners.
TINA steps into the middle of the road, watching the black silk fall out of the sky to shroud the surrounding buildings in darkness.
TINA It’s Grindelwald. He’s calling his followers.
We pan up one length of flowing black silk until we achieve an aerial view of Paris. The entire city is being covered in GRINDELWALD’S dark banners.
Fantastic Beasts: The Crimes of Grindelwald - The Original Screenplay, Scene 81
"Newt blows some dude following him back with huge winds while everyone walks normally past him."
The Muggles can see when Stebbins gets caught in the hurricane but just find it amusing.
SCENE 26
EXT. LONDON BACK STREET—EVENING
NEWT Apparates and walks on briskly beneath an increasingly stormy sky. Seconds later, STEBBINS, an Auror, Apparates some yards behind him. They have been playing this game for an hour. NEWT turns a corner into a darker alleyway, peers back around the corner, and points his wand back at STEBBINS.
NEWT (sotto voce) Ventus.
STEBBINS is immediately caught in a hurricane for one. To the confusion and amusement of passing Muggles, his hat flies away, he is almost knocked off his feet, and cannot proceed.
Fantastic Beasts: The Crimes of Grindelwald - The Original Screenplay
Considering the film's events it's also likely Muggles saw the flames that Grindelwald had conjured to fight the Auror's with. However, the scene is mentioned to take place at night, likely quite late on, so less Muggles would have been about. Unfortunately, the official screenplay is rather brief in it's description here so we don't really get an indication if a Muggle would have seen it but I'd imagine it was likely.
SCENE 115
EXT. PÈRE LACHAISE CEMETERY—A MINUTE LATER—NIGHT
NEWT and THESEUS, TINA with JACOB, and KAMA with NAGINI all Apparate out from the amphitheater. The black fire pursues them like a many-headed hydra, erupting out of every mausoleum.
FLAMEL arrives at last.
The cemetery is on the verge of destruction. The fire GRINDELWALD has unleashed is out of control. It forms dragon-like creatures intent on annihilation.
[...]
NEWT and THESEUS, TINA with JACOB, and KAMA with NAGINI all Apparate out from the amphitheater. The black fire pursues them like a many-headed hydra, erupting out of every mausoleum.
FLAMEL arrives at last.
The cemetery is on the verge of destruction. The fire GRINDELWALD has unleashed is out of control. It forms dragon-like creatures intent on annihilation.
And at last, their purifying fire drives GRINDELWALD’S back. The entrances to the underground lair are sealed.
They have saved the city.
Fantastic Beasts: The Crimes of Grindelwald - The Original Screenplay
It is also likely at least some Muggles would have seen Credence as the Obscurus attacking Grimmson but no mention is made of this. It is all the more likely considering the Obscurus rips apart the attic and roof of the building for people to see what is happening.
Now the Obscurus expands in fury, smashing apart the attic like a tornado.
GRIMMSON smiles up at the Obscurus: We’ll meet again. He Disapparates.
Mingling with the debris of the destroyed attic, the Obscurus slams inward and CREDENCE re-forms. He stands looking down at the tiny body.
Fantastic Beasts: The Crimes of Grindelwald - The Original Screenplay, Scene 56
"Are they just not going to do that this time around, did they just not have time to worry about it?"
As for why they don't Obliviate the Muggles that saw these events, well, they just had more important things to do. Note that they are tracking down and trying to face Grindelwald and if they don't catch him worse things will happen than just seeing a Zouwu or a man caught in some extremely localised wind.
