The new direction for the Ministry fit with Umbridge’s ideology.
Umbridge had always sucked up to the Minister of Magic, even when that was Fudge and the Ministry was entirely separate from the Dark Lord, so she simply remained with the Ministry rather than joining or aligning herself with the Dark Lord or the Death Eaters. However, their ideology, and the Ministry under their rule, suited Umbridge’s personal ideology much better. She was promoted to the head of the newly formed Muggle-born Registration Commission, and was able to freely write the laws she’d wanted to all along.
“The plaque beneath it read:
Dolores Umbridge
Senior Undersecretary to the Minister
Below that, a slightly shinier new plaque read:
Head of the Muggle-born Registration Commission”
- Harry Potter and the Deathly Hallows, Chapter 13 (The Muggle-Born Registration Commission)
Umbridge was quite happy in her role purging the wizarding world of Mudbloods, as evidenced by the strong Patronus she produced there.
“The moment he had passed the place where the Patronus cat patrolled he felt the change in temperature: it was warm and comfortable here. The Patronus, he was sure, was Umbridge’s, and it glowed brightly because she was so happy here, in her element, upholding the twisted laws she had helped to write.”
- Harry Potter and the Deathly Hallows, Chapter 13 (The Muggle-Born Registration Commission)
She also was able to openly want to harm Harry, which was now sanctioned by the Ministry.
“He had an idea he knew who that was, and sure enough, as he straightened up and glanced around the office for fresh hiding places, he saw a poster of himself on the wall, with the words UNDESIRABLE NO. 1 emblazoned across his chest. A little pink note was stuck to it, with a picture of a kitten in the corner. Harry moved across to read it and saw that Umbridge had written ‘To be punished’.”
- Harry Potter and the Deathly Hallows, Chapter 13 (The Muggle-Born Registration Commission)
She truly hated half-breeds like werewolves and merpeople, and wrote legislation against them even when the Ministry wasn’t under control of the Dark Lord.
“Does Lupin know her?’ asked Harry quickly, remembering Umbridge’s comments about dangerous half-breeds during her first lesson.
‘No,’ said Sirius, ‘but she drafted a bit of anti-werewolf legislation two years ago that makes it almost impossible for him to get a job.’
Harry remembered how much shabbier Lupin looked these days and his dislike of Umbridge deepened even further.
‘What’s she got against werewolves?’ said Hermione angrily.
‘Scared of them, I expect,’ said Sirius, smiling at her indignation. ‘Apparently, she loathes part-humans; she campaigned to have merpeople rounded up and tagged last year, too.”
- Harry Potter and the Order of the Phoenix, Chapter 14 (Percy and Padfoot)
She also genuinely hated Mudbloods, as hinted at in her content at sending them off to the Dementors.
“This is your final warning,’ said Umbridge’s soft voice, magically magnified so that it sounded clearly over the man’s desperate screams. ‘If you struggle, you will be subjected to the Dementor’s kiss.’
The man’s screams subsided, but dry sobs echoed through the corridor.
‘Take him away,’ said Umbridge.”
- Harry Potter and the Deathly Hallows, Chapter 13 (The Muggle-Born Registration Commission)
The J.K. Rowling writing on Pottermore about Umbridge says her hatred of Muggles went back before she even joined the Ministry.
Dolores’s parents were unhappily married, and Dolores secretly despised both of them: Orford for his lack of ambition (he had never been promoted, and worked in the Department of Magical Maintenance at the Ministry of Magic), and her mother, Ellen, for her flightiness, untidiness, and Muggle lineage.
- Dolores Umbridge (Pottermore)
That same writing says she was both prejudiced and good at sucking up, convincing her bosses that she was worthy of promotion.
An accomplished witch, Dolores joined the Ministry of Magic directly after she left Hogwarts, taking a job as a lowly intern in the Improper Use of Magic Office. Even at seventeen, Dolores was judgemental, prejudiced and sadistic, although her conscientious attitude, her saccharine manner towards her superiors, and the ruthlessness and stealth with which she took credit for other people’s work soon gained her advancement.
- Dolores Umbridge (Pottermore)
It goes on to state (as evidence in the books also shows) that she enjoyed working in the Ministry more when it was under the Dark Lord’s control.
Dolores was soon enjoying life at the Ministry more than ever. When the Ministry was taken over by the puppet Minister Pius Thicknesse, and infiltrated by the Dark Lord’s followers, Dolores was in her true element at last. Correctly judged, by senior Death Eaters, to have much more in common with them than she ever had with Albus Dumbledore, she not only retained her post but was given extra authority, becoming Head of the Muggle-born Registration Commission, which was in effect a kangaroo court that imprisoned all Muggle-borns on the basis that they had ‘stolen’ their wands and their magic.
- Dolores Umbridge (Pottermore)
Overall, Umbridge had no reason to fight against the Dark Lord controlling the Ministry - the Ministry was doing exactly what she wanted.
It’s unclear if she actually knew who was behind the changes.
Umbridge certainly enjoyed the new regime - what was less clear is if she knew it was actually orchestrated by the Dark Lord. The Dark Lord took over the Ministry very quietly, installing a puppet Minister and not handling any of the Ministry business himself. The Ministry also wasn’t staffed by the type of well-known Death Eaters that the majority of the wizarding world knew were Death Eaters. The only one working at the Ministry under his control who was even shown to be a Death Eater was Yaxley, and he wasn’t a particularly notorious Death Eater. He could have easily gotten a plausible cover story for his presence at the Astronomy Tower, and wasn’t a known Death Eater before that. Snape refers to him as one of the Death Eaters who was free to but didn’t try to find the Dark Lord, meaning he wouldn’t have been convicted.
“You ask why I did not attempt to find him when he vanished. For the same reason that Avery, Yaxley, the Carrows, Greyback, Lucius,’ he inclined his head slightly to Narcissa, ‘and many others did not attempt to find him.”
- Harry Potter and the Half-Blood Prince, Chapter 2 (Spinner’s End)
Other than Yaxley, the Ministry wizards under the Dark Lord’s regime were simply Ministry wizards who could serve his purpose, placed under the Imperius Curse or naturally willing to enforce pure-blood laws.