I am creating an aasimar character who is devoted not only to her father's (celestial) faith but also to the preservation of nature. However, while making this character, I realized that, although I can find a lot of information about who these races are and what they do (as well as hidden lore about blood aasimar and the birth of their celestial parents), I have not found much about the deities celestials serve.

Do celestials/aasimars all serve one deity, or if they can serve any deity as long as their alignment is good?

More specifically for my case, I am considering Arawai, goddess of fertility, as she's about life and nature, though she's a Neutral Good deity from the Eberron setting.

Celestials and aasimar can be connected to any (or no) deity

To start with, celestials are simply a specific type of creature. An extremely wide range of creatures fit into the category of celestial including some which are entirely disconnected from deities in their creation or patronage. One example is the Pegasus which simply hails from a plane wherein some deities reside:

Pegasi trace their origins to the Olympian Glades of Arborea, where they soar through the skies of that plane and serve as faithful mounts to the Seldarine, the pantheon of elven gods.

Aasimar are also just influenced by planar power (not necessarily power from any deity) through ancestry:

They are descended from humans with a touch of the power of Mount Celestia

Many aasimar do serve the ideals of law and good, but fallen aasimar do exist, and no single deity can claim inherent ownership of any aasimar.

In conclusion, any deity is eligible to be connected to a celestial or aasimar.

To reference Volo's Guide to Monsters specifically (see page 105)

Aasimar are placed in the world to serve as guardians of law and good.
Their patrons expect them to strike at evil, lead by example, and
further the cause of justice. From an early age, an aasimar receives
visions and guidance from celestial entities via dreams. These dreams
help shape an aasimar, granting a sense of destiny and a desire for
righteousness. Each aasimar can count a specific celestial agent of
the gods as a guide. This entity is typically a deva, an angel who
acts as a messenger to the mortal world.

Also found on the same page of Volo's Guide to Monsters:

Aasimar bear within their souls the
light of the heavens. They are descended from humans with a touch of
the power of Mount Celestia, the divine realm of many lawful good
deities. Aasimar are born to serve as champions of the gods, their
births hailed as blessed events. They are a people of otherworldly
visages, with luminous features that reveal their celestial heritage.

From all of this we can gather that Aasimars are descendants of various deities, and are guided by various others, so basically it's up to you (or your DM) what dieties have ties to any given Aasimar.

There are no rules for worshiping gods, but likely a lawful good god

Aasimar are found in the Volo's Guide to Monsters and the relevant part of their description is below:

Aasimar bear within their souls the light of the heavens. They are descended from humans with a touch of the power of Mount Celestia, the divine realm of many lawful good deities. Aasimar are born to serve as champions of the gods, their births hailed as blessed events.

The description is "champions of the gods", gods in general with no specific reference made to a particular deity. The only guidance we are given is that Mount Celestia is home to mostly lawful good deities. The next section also assumes this:

Aasimar are placed in the world to serve as guardians of law and good. Their patrons expect them to strike at evil, lead by example, and further the cause of justice.

So although this is all just descriptive text the assumption is that most Aasimar will follow a lawful good deity. This doesn't have to be the case however, the description goes on to mention their conflicted souls:

Despite its celestial origin, an aasimar is mortal and possesses free will. Most aasimar follow their ordained path, but some grow to see their abilities as a curse. These disaffected aasimar are typically content to turn away from the world, but a few become agents of evil. In their minds, their exposure to celestial powers amounted to little more than brainwashing.

Remember however, that this is only guidance and there is no restriction on the alignment, deity or class of any race in 5th edition. What gods exist in your world is up to your DM and you can work with them to decide which suits your character best. If you choose to be an archetypical aasimar that would likely be a lawful good god but you aren't required to follow this.