(At times) in Ramadan the Prophet (ﷺ) used to take a bath in the morning not because of a wet dream and would continue his fast.
Sahih al-Bukhari Book 30, Hadith 38
← Previous Hadith (daughter of Um Salama) that her mother said, "While I was (lying) with Allah's Messenger (ﷺ) underneath a woolen sheet, I got the menstruation, and then slipped away and put on the clothes (which I used to wear) in menses. He asked, "What is the matter? Did you get your menses?" I replied in the affirmative and then entered underneath that woolen sheet. I and Allah's Messenger (ﷺ) used to take a bath from one water pot and he used to kiss me while he was fasting."

Sahih al-Bukhari Book 30, Hadith 37 Next Hadith → My father and I went to `Aisha and she said, "I testify that Allah's Messenger (ﷺ) at times used to get up in the morning in a state of Janaba from sexual intercourse, not from a wet dream and then he would fast that day." Then he went to Um Salama and she also narrated a similar thing.

Sahih al-Bukhari Book 30, Hadith 39