How do I implement option buttons and change the button color in PyGame?

When you draw the button, you have to set the color dependent on the global variable clicked:

def draw_button(self):

    global clicked
    
    # get mouse position
    pos = pygame.mouse.get_pos()

    # create pygame Rect object for the button
    button_rect = Rect(self.x, self.y, self.width, self.height)

    # check mouseover and clicked conditions
    hover = button_rect.collidepoint(pos)
    if hover and pygame.mouse.get_pressed()[0] == 1:
        clicked = not clicked

    color = self.button_col
    if clicked:
        color = self.click_col
    elif hover:
        color = self.hover_col

    pygame.draw.rect(screen, color, button_rect)

Anyway, that won’t satisfy you, because pygame.mouse.get_pressed() returns a list of Boolean values ​​that represent the state (True or False) of all mouse buttons. The state of a button is True as long as a button is held down.
You have to use MOUSEBUTTONDOWN event. The MOUSEBUTTONDOWN event occurs once when you click the mouse button and the MOUSEBUTTONUP event occurs once when the mouse button is released. The pygame.event.Event() object has two attributes that provide information about the mouse event. pos is a tuple that stores the position that was clicked. button stores the button that was clicked.

---

If you have multiple buttons that you have to interact with each other, a single clicked status is not enough. You need a separate “clicked” state for each button. If the clicked state of 1 button becomes True, the states of the other keys must be set to False. I recommend to implement a RadioButton class for this.

See also Mouse and Sprite.

Minimal example:
repl.it/@Rabbid76/PyGame-RadioButton

import pygame

class RadioButton(pygame.sprite.Sprite):
    def __init__(self, x, y, w, h, font, text):
        super().__init__() 
        text_surf = font.render(text, True, (0, 0, 0))
        self.button_image = pygame.Surface((w, h))
        self.button_image.fill((96, 96, 96))
        self.button_image.blit(text_surf, text_surf.get_rect(center = (w // 2, h // 2)))
        self.hover_image = pygame.Surface((w, h))
        self.hover_image.fill((96, 96, 96))
        self.hover_image.blit(text_surf, text_surf.get_rect(center = (w // 2, h // 2)))
        pygame.draw.rect(self.hover_image, (96, 196, 96), self.hover_image.get_rect(), 3)
        self.clicked_image = pygame.Surface((w, h))
        self.clicked_image.fill((96, 196, 96))
        self.clicked_image.blit(text_surf, text_surf.get_rect(center = (w // 2, h // 2)))
        self.image = self.button_image
        self.rect = pygame.Rect(x, y, w, h)
        self.clicked = False
        self.buttons = None

    def setRadioButtons(self, buttons):
        self.buttons = buttons

    def update(self, event_list):
        hover = self.rect.collidepoint(pygame.mouse.get_pos())
        for event in event_list:
            if event.type == pygame.MOUSEBUTTONDOWN:
                if hover and event.button == 1:
                    for rb in self.buttons:
                        rb.clicked = False
                    self.clicked = True
        
        self.image = self.button_image
        if self.clicked:
            self.image = self.clicked_image
        elif hover:
            self.image = self.hover_image


pygame.init()
window = pygame.display.set_mode((300, 300))
clock = pygame.time.Clock()
font50 = pygame.font.SysFont(None, 50)

radioButtons = [
    RadioButton(50, 40, 200, 60, font50, "option 1"),
    RadioButton(50, 120, 200, 60, font50, "option 2"),
    RadioButton(50, 200, 200, 60, font50, "option 3")
]
for rb in radioButtons:
    rb.setRadioButtons(radioButtons)
radioButtons[0].clicked = True

group = pygame.sprite.Group(radioButtons)

run = True
while run:
    clock.tick(60)
    event_list = pygame.event.get()
    for event in event_list:
        if event.type == pygame.QUIT:
            run = False 

    group.update(event_list)

    window.fill(0)
    group.draw(window)
    pygame.display.flip()

pygame.quit()
exit()