<t t-out="step_specific_values['main_button']"/>

is defined in 

<template id="navigation_buttons" ... />

<a role="button" name="website_sale_main_button" ... />

is defined in

<template id="extra_info" ... />

and

<template id="navigation_buttons" ... />

Now, none of these actually hold a string 'Checkout'. Instead, Odoo uses a list of tuples that seems rather complex at first sight to generate the buttons for each sidebar, grouped in (the actual checkout) steps.

So, while you theoretically could just replace <t t-out="step_specific_values['main_button']"/> in website_sale.step_specific_values (not website_sale.checkout!) you should rather inherit the website model and change the behavior of _get_checkout_step_list() like this:

from odoo import models
from odoo.tools.translate import LazyTranslate
_lt = LazyTranslate(__name__)


class Website(models.Model):
    _inherit = 'website'

    def _get_checkout_step_list(self):
        steps = super()._get_checkout_step_list()
        # You may want to adjust the conditions to more precisely limit the 
        #  string replacement to website_sale.cart
        for _, data in steps:
            if 'main_button' in data and str(data['main_button']) == 'Checkout':
                data['main_button'] = _lt('Book Appointment')
        return steps

Else, you're potentially overriding the labels of other steps too.