@tafiatilik that is a relatively new phone and the issue could be a. related to a bad battery and b. related to a bad screen. From what you are describing, I would replace the display assembly and the battery, then re-evaluate. There is always the possibility that this is a board error but that will have to be ruled out.
Since iFixit does not yet have a guide for this, use teh one [https://www.nadiemellamagallina.com/en/manuales/smartphones-1/samsung-4/samsung-galaxy-s23-ultra-1415/pantalla-completa-12881|from here] It was written in Spanish so use a browser that does the translation for you, if needed. For a replacement, get the disparately that already has the midframe on since that will make it far easier than just a single display.