Manipulating public opinion, power struggles, exchange of interests, shifting conflicts...
Winning over some, dividing others, suppressing a few...
These are standard tactics for politicians, and the Magic Realm is no exception. Wherever there are people, there is society, and wizards aren't any more equipped than Muggles with extra arms or legs... Actually, to be precise, apart from knowing some magic, normal wizards aren't essentially different from normal Muggles.
And Dumbledore isn't unfamiliar with this at all. After all, raw power alone can't make you the head of the International Confederation of Wizards.
It should be noted that back in the day, Grindelwald really went through great lengths to campaign for the position, only to fail at the last hurdle. When Dumbledore rose to power, it was impossible for him to have no competitors or opponents, because no one can satisfy everyone. So, in his youth, Dumbledore also made efforts for those powers.
He hoped to change the world with these efforts.
Unfortunately, he couldn't master the art. Compared to delving into politics, dedicating himself to academic pursuits or teaching and nurturing others made him more fulfilled.
Then, as he grew older and gained more experience, he became increasingly weary of these matters.
Thus, he stepped away from politics, and most of his titles became merely decorative, because those positions needed a strong mascot. Dumbledore was more than happy to be such a mascot. As he said, if he could still change the world, he was willing to make some sacrifices for it.
However, this was a form of compromise in itself.
He was signaling to others, "I'm old, I no longer wish to compete, as long as you don't do anything too outrageous, I won't interfere"—it's just that, whether due to paranoia or a strong territorial instinct, the current Minister of Magic of the United Kingdom, Cornelius Fudge, still stubbornly believes Dumbledore is coveting his position.
...What a bother.
He hadn't intended to meddle in Ministry of Magic affairs, thinking that in time, Fudge would understand his good intentions. But that fat man kept conjuring up bizarre notions and started scheming against him, increasingly crossing the line lately.
The decision to place Dementors around Hogwarts might have been a whimsical idea of Fudge's, but his influence on this matter has been ongoing for some time.
Why were Dementors deployed from Azkaban to capture Sirius? Essentially, it was due to public pressure. If Fudge wanted to hold on to his position, he needed to catch the fugitive quickly.
The reason for using Dementors as the captors is that the Ministry of Magic lacks manpower, which is due to Fudge's longstanding apprehension towards the current Head of the Auror Office. He's been suppressing the Auror Office for a long time, clearly viewing Dumbledore as not his only imagined enemy.
...Wait, maybe it's not imagined at all.
Anyway, the root cause of this situation is essentially Fudge's fear of losing power and his thirst for more.
Whether in times of peace or times of war, a leader with an extreme hunger for power is a double-edged sword—it can lead to social progress if you're lucky, but could bring about chaos if you're not... But the issue now is, Cornelius Fudge isn't even fit to be called a double-edged sword.
He's just a wooden stirring stick.
And both ends of the stick are covered in filth, grabbing either end will disgust you.
So, Dumbledore decided to take action... Oh, but not to grab the filth.
The simplest way to make someone comply is to make them believe they have options...
...Wow, wait, (°〇°) no.
I can't say more.
In short, Dumbledore simply offered Fudge a few choices, a few simple options, including stepping down from his position or staying put but listening to me. Naturally, Dumbledore's words weren't so direct, just hinting here and there that he could have Fudge removed from his seat anytime.
Fudge had been well aware of this, just unwilling to believe it until now.
And he was horrified to discover that the wizarding world, which assumed Dumbledore's strength was waning due to age, was still intensely powerful—he was able to take control of all the Dementors stationed to monitor Hogwarts!
This discovery left Fudge's head buzzing with shock.
Bear in mind, the Ministry of Magic once expended considerable effort to manage those dreaded creatures.
Before becoming the Wizard Prison of the United Kingdom, Azkaban was the private domain of an evil wizard named Ekrizdis. This wizard would lure Muggles to his island and conduct experiments on them until death. It was only after Ekrizdis died that the Concealment Charm he used on his fortress and island began to lose its power, making the island known to the Ministry of Magic. Since then, Azkaban had been deserted until 1718 when, with the passage of the Wizarding Secrecy Law, the then Minister of Magic proposed turning Azkaban into a new Wizard Prison, utilizing Capacious Extremis to expand its interior.