Would

[Bookworm]

Perhaps now the gods had decided the time was ripe for him to gain his vengeance, after all the times they had ensured his attempts had failed. Hui would offer a prayer to Horus as he travelled across the waters.

Какую роль(часть речь) тут играет would?

[Bookworm]

Вот тут тоже непонятно:

Dust clouded from his wheels, and then an outrider overtook Khyan and Hui saw it was his brother. Qen had his head low over the beast’s neck, his dark features cold with determination. The Ka Stone would be burning in his mind.

[Yety]

Hui would offer a prayer to Horus as he travelled across the waters

По всей видимости, этот would - прошедшая форма модального will в значении повторяющегося действия:

8. Used to express repeated or habitual action in the past:
Every morning we would walk in the garden.

3. used as an auxiliary to describe a past action as being accustomed or habitual:
every day we would go for walks.

4. (used to express repeated or habitual action in the past):
We would visit Grandma every morning up at the farm.

would v. used toПоказать

2. talking about the past
You can use would to talk about something that happened regularly in the past but no longer happens.

We would normally spend the winter in Miami.
She would often hear him singing.
Used to has a similar meaning.

She used to visit them every Sunday.
In the afternoons, I used to read.
However, used to can also be used to talk about states and situations that existed in the past but no longer exist. You cannot use 'would' like this. You can say, for example, 'She used to work there'. Don't say 'She would work there'

I used to be quite overweight.
...
When would not is used to talk about something that happened in the past, it means that someone refused to do something.

They just would not believe what we told them.
I asked him to come with me, but he wouldn't.

Это употребление would - всего лишь прошедшая форма модального will в таком значении:

6. Used to indicate customary or habitual action:
People will talk.

6. am (is, are, etc.) accustomed to, or do usually or often:
She would write for hours at a time.

Можно обратить внимание, что в последнем примере прошедшая форма would иллюстрирует употребление глагола will в настоящем.)

Осталось прояснить, предполагает ли контекст какую-либо повторяемость этого молитвенного обращения.))

[Yety]

The Ka Stone would be burning in his mind.

Здесь какой-то оттенок вышеуказанного употребления с длительным инфинитивом, не выделенного в отдельное значение в словарях. Предполагает кяп настойчивость, упорство, продолжительность процесса.
"Пепел Клааса всё стучал в моё сердце..."

PS И всё это, конечно, первые производные от буквального значения will "желать, изволить".

[Yety]

Осталось прояснить, предполагает ли контекст какую-либо повторяемость этого молитвенного обращения.))

Похоже, не предполагает..
Так что, по всей видимости, слажал. Хорошо, что есть кому поправить.))

Perhaps now the gods had decided the time was ripe for him to gain his vengeance, after all the times they had ensured his attempts had failed. Hui would offer a prayer to Horus as he travelled across the waters.

Судя по всему, это обычный future-in-the-past. Если проверить переносом в настоящее:

Perhaps now the gods haVE decided the time IS ripe for him to gain his vengeance, after all the times they haVE ensured his attempts haVE failed. Hui WILL offer a prayer to Horus as he travellS across the waters.

SORRY.

Dust clouded from his wheels, and then an outrider overtook Khyan and Hui saw it was his brother. Qen had his head low over the beast’s neck, his dark features cold with determination. The Ka Stone would be burning in his mind.

Здесь надо бы контексту побольше.
Есть мнение, что это модальный would в значении предположения.
"Камень, походу, будет гореть у него во лбу.."

6. Used to express presumption or expectation:
That would be Steve at the door.
7. Used to indicate uncertainty:
He would seem to be getting better.