Mysterious voltage drop when ESP32 board is connected

[ESP_Sprite]

Linear regulation (including the solution with resistors you chose earlier, given you choose resistors low enough to work) will always burn off the excess voltage as heat; no way around that. Look into switched mode power supplies for something that generates less hear; you can get modules like the Murata 7805SR that are plug-in replacements for the 7805 you already use.