Here’s something interesting about swans, or hamsas, as mentioned in the Nada Bindu Upanishad, taken from The Voice of Silence by H.P. Blavatsky

Kala Hamsa, the “Bird” or Swan… “A is considered to be its (the bird Hamsa’s) right wing, U, its left, M, its tail, and the Ardha-matra (half metre) is said to be its head.”
AUM

Some Sanskrit mystics locate seven planes of being, the seven spiritual lokas or worlds within the body of Kala Hamsa, the Swan out of Time and Space, convertible into the Swan in Time, when it becomes Brahma instead of Brahma (neuter).

Aum, Om, ॐ

And from the Hamsa Upanishad :

…one should contemplate upon Hamsa as the Āṭmā in his heart. Agni and Soma are its wings (right and left sides); Omkāra is its head; Ukāra and binḍu are the three eyesand face respectively; Ruḍra and Ruḍrāṇī (or Ruḍra’s wife) are the feet kanthaṭa (or the realisation of the oneness of jīvāṭmā or Hamsa, the lower self with Paramāṭmā or Paramahamsa, the Higher Self) is done in two ways, (samprajñāṭaand asamprajñāṭa).

More mention of swans in the Rig Veda:

Book 5, Hymn LXXVIII. Aśvins.

1. YE Aśvins, hither come to us: Nāsatyas, be not disinclined.
Fly hither like two swans unto the juice we shed.
2. O Aśvins, like a pair of deer, like two wild cattle to the mead:
Fly hither like two swans unto the juice we shed.
3. O Aśvins rich in gifts, accept our sacrifice to prosper it:
Fly hither like two swans unto the juice we shed.

HYMN XXXV. Asvins.  8: Ye fly like swans, like those who travel on their way; like buffaloes ye seek the Soma we have shed.
Accordant, of one mind with Surya and with Dawn, come thrice, O Asvins, to our home.

HYMN XLV. Asvins: 4: The swans ye have are friendly, rich in store of mcath, gold-pinioned, strong to draw, awake at
early morn, Swimming the flood, exultant, fain for draughts that cheer: ye come like flies to our libations of-the
meath.

HYMN CLXIII. The Horse: 5: With brightly-flarning kine whose udders swell with milk, idth glittering lances on your
unobstructed paths, Put forth their strength, like swans in lengthened order, when they, the Steeds, have reached the

heavenly causeway. 

HYMN CLXIII. The Horse: 10: Symmetrical in flank, with rounded haunches, mettled like heroes, the Celestial Coursers
Put forth their strength, like swans in lengthened order, when they, the Steeds, have reached the heavenly causeway.

HYMN LIX. Maruts. 7: Decking the beauty of their forms in secret the Swans with purple backs have flown down hither.
Around me all the Company hath settled, like joyous Heroes glad in our libation.

HYMN XCVII. Soma Pavamana: 8: The Swans, the Vrsaganas from anear us have brought their restless spirit to our dwelling.
Friends come to Pavamana meet for praises, and sound in concert their resistless music. Ye singers, with the Gods, sages who look on men, ye Kutikas drink up the Soma’s savoury meath.

HYMN LIII. Indra, Parvata, Etc.: 10: Like swans, prepare a song of praise with pressing-stones, glad in your hymns with juice poured
forth in sacrifice.

The Rig Veda: Ralph T.H. Griffith English translation

Pdf format