How can the Buddha (after he was enlightened) reflect that he was not at ease and then became at ease in seclusion?

All of the following quotes come from MN 44.

One of the five aggregates is feeling (vedana) or sensations.

It's a mental process.

Perception and feeling are mental. They’re tied up with the mind, that’s why perception and feeling are mental processes.”

There are 3 types of feeling.

“There are three feelings: pleasant, painful, and neutral feeling.”

“What are these three feelings?”

“Anything felt physically or mentally as pleasant or enjoyable. This is pleasant feeling. Anything felt physically or mentally as painful or unpleasant. This is painful feeling. Anything felt physically or mentally as neither pleasurable nor painful. This is neutral feeling.”

“What is pleasant and what is painful in each of the three feelings?”

“Pleasant feeling is pleasant when it remains and painful when it perishes. Painful feeling is painful when it remains and pleasant when it perishes. Neutral feeling is pleasant when there is knowledge, and painful when there is ignorance.”

The Buddha has discarded identity view or self view.

“It’s when an educated noble disciple has seen the noble ones, and is skilled and trained in the teaching of the noble ones. They’ve seen good persons, and are skilled and trained in the teaching of the good persons. They don’t regard form as self, self as having form, form in self, or self in form. They don’t regard feeling … perception … choices … consciousness as self, self as having consciousness, consciousness in self, or self in consciousness. That’s how identity view does not come about.”

So, based on your quote, the Buddha experienced painful feelings from the six sense media but it doesn't mean that he clung to them, or had self view associated with them, or suffered from them. These painful feelings did not give rise to aversion or hate (dosa), in the absence of clinging and defilements.

Furthermore, an enlightened being is inclined to seclusion.

“But ma’am, when a mendicant has emerged from the attainment of the cessation of perception and feeling, what does their mind slant, slope, and incline to?”

“Their mind slants, slopes, and inclines to seclusion.”

Living arahants having five aggregates still functional but without defilements and clinging is discussed in Iti 44.

And what is the Unbinding property with fuel remaining? There is the case where a monk is an arahant whose fermentations have ended, who has reached fulfillment, finished the task, laid down the burden, attained the true goal, ended the fetter of becoming, and is released through right gnosis. His five sense faculties still remain and, owing to their being intact, he is cognizant of the agreeable & the disagreeable, and is sensitive to pleasure & pain. His ending of passion, aversion, & delusion is termed the Unbinding property with fuel remaining.

And what is the Unbinding property with no fuel remaining? There is the case where a monk is an arahant whose fermentations have ended, who has reached fulfillment, finished the task, laid down the burden, attained the true goal, ended the fetter of becoming, and is released through right gnosis. For him, all that is sensed, being unrelished, will grow cold right here. This is termed the Unbinding property with no fuel remaining."
Iti 44

In many traditions, attainment is not regarded as a permanent mental state, but requires constant practice. This is why, for example, Dogen Zenji wrote: "we do not practice to become enlightened, we practice because we are enlightened".

Before his enlightenment the Buddha spent extended periods alone in the forests:

“Such was my seclusion that I would plunge into some forest and live there. If I saw a cowherd, shepherd, grass-cutter, wood-gatherer or forester, I would flee so that they would not see me or me them” (M.I,79).

Even after attaining enlightenment he would occasionally go into solitude. In the Saüyutta Nikàya he is recorded as saying:

“I wish to go into solitude for half a month. No one is to come to see me except the one who brings my food” (S.V,12).

Many teachers from different lineages lived in physical seclusion before they took students. Famous examples include Bodhidharma & Hanshan.

Similar to Andrei's answer I note (as fact) that it's a narration of what the Buddha thought, not what he said.

Going even further I might speculate that it's similar to Mother's saying to children, "While sitting in his office, Dad thought, 'Isn't it good that the children are playing quietly, and doing their homework'" -- i.e. it's said to convey a message, needn't be understood (except perhaps by children in question) as a direct and verbatim quote.

Lastly I don't get the impression from the suttas that the Buddha had no preferences. Apparently he preferred what's ethical, skillful, conditions for successful practice, compassionate, etc. (and that doctrine may be easier to understand than a doctrine like, "lol, nothing exists: good, bad, it's all the same..." -- especially for inter-personal relationships).

I wonder whether we're meant to see literally-all the Buddha's actions as motivated only by this kind of preference and this kind of intent -- so much so that any spark of evidence to the contrary (like a preference for avoiding quarrels) is seen as questionable and demanding an explanation.

I suppose it is possible -- that the basis for the preference is that his hanging around while people quarrel would be unskillful.

I'm not sure -- which is why I think this is a good question and which I hope someone answers.

Canonically perhaps there are specific types of preference which an arahant is free from:

• Sensual desire (kāmacchando)
• Desire for existence and rebirth, both material and immaterial (rūparāgo and arūparāgo)

To be logical perhaps it would be enough to explain that the preference isn't based on one of these fetters.

Obviously that entire text was authored by someone else, speaking about the Buddha in the third person.

In my understanding, the part about the Buddha leaving the quarreling Sangha is based on real events, while the thoughts going through Buddha's mind must be the author's conjecture.

To be clear, I'm not saying Buddha did not leave the quarreling Sangha for seclusion. That part is in accordance with Dharma. I'm saying, the part that represents Buddha's thoughts as speaking in terms of "before I was X and now I'm Y" must be a simplification and not the exact thought that crossed the Buddha's mind. Why? Because buddhas don't think in such terms. Why don't they? Because that would be "I-making".