Your VueJS code is correct, the problem is that TailwindCSS doesn't know the classes. That's because TailwindCSS analyses the HTML / CSS in order to keep only the existing classes.
You have some dynamic classes and TailwindCSS doesn't add automatically dynamic classes (the variable isn't converted to its value). You need to declare each dynamic class in the safelist and also the corresponding colors to each class.
https://tailwindcss.com/docs/content-configuration#safelisting-classes
For example you have the bg-accent-base and the corresponding color is accent with its variations base, strong, weak, ...
https://tailwindcss.com/docs/customizing-colors#color-object-syntax
/** @type {import('tailwindcss').Config} */
module.exports = {
content: [
"./resources/**/*.blade.php",
"./resources/**/*.js",
"./resources/**/*.vue",
],
safelist: [
// background images
'bg-accent-base',
'bg-accent-strong',
'bg-accent-weak',
],
theme: {
colors: {
'accent': {
base: '#317917',
strong: '#317917',
weak: '#317917',
},
},
extend: {
backgroundImage: {
},
},
fontFamily: {
},
},
plugins: [],
}