Answer
Is it correct to say that it is the appearance day of Lord Jagannath? Not necessarily in the way we usually understand an appearance day on Earth.
First, let us understand what Snana-yatra is.
Once a year, on the auspicious occasion of Snana Purnima, the wooden deities of Lord Jagannath, Baladeva, and Subhadra are brought out from the altar in a special ceremony. They are taken to a raised platform outside the temple, known as the Snana-vedi, where devotees gathered from all around can have darshan of the Lord and witness the ceremonial bathing ceremony.
Ordinarily, the main deities are not bathed directly every day. Instead, the bathing service is offered to their reflection in a mirror. Because the deities are very large and sacred, the full ceremonial bathing of the principal deities takes place only once a year, on Snana Purnima. Therefore, Snana-yatra is the annual ceremonial bathing festival of the Lord.
Regarding the appearance day of Lord Jagannath, I am not aware of any specific date that is traditionally celebrated in Jagannath Puri as the appearance day of the Lord. For the devotees of Lord Jagannath, every day is a festival because the Lord eternally resides in the spiritual atmosphere of the temple.
In spiritual life, every day is an occasion for celebration. Although different festivals may have different names and special observances, the worship of the Lord continues joyfully every single day.
Every day, the Lord is awakened, bathed, dressed, decorated, offered delicious preparations, and served in numerous ways. Especially in the Jagannath Puri temple and other ancient temples, there is a very detailed and rigorous schedule of devotional services. From early morning, often beginning around four o'clock, until late at night, many different services are offered continuously.
The servants of the Lord remain constantly engaged in caring for Him with great devotion and attention. This continuous loving service is one of the special features of deity worship in the temple.
As for the specific historical date connected with the manifestation or installation of the Jagannath deities, I do not personally know that information. It may be available from devotees who serve in Jagannath Puri or from authentic scriptures and historical records that describe the details of Lord Jagannath's worship and temple traditions.
