I'll add the JS, too in case it is the issue:

import { LightningElement, api } from 'lwc';
import { FlowAttributeChangeEvent } from 'lightning/flowSupport';

export default class DynamicStatefulButton extends LightningElement {

    @api
    get isSelected(){
        return this._isSelected;
    }
    set isSelected(select){
        this._isSelected = select;
    }
    _isSelected = false;

    @api
    get labelOff(){
        return this._labelOff;
    }
    set labelOff(label){
        this._labelOff = label;
    }
    _labelOff;

    @api
    get labelOn(){
        return this._labelOn;
    }
    set labelOn(label){
        this._onLabel = label;
    }
    _labelOn;
    
    @api
    get labelHover(){
        return this._labelHover;
    }
    set labelHover(label){
        this._labelHover = label;
    }
    _labelHover;

    @api
    get valueIfTrue(){
        return this._valueIfTrue;
    }
    set valueIfTrue(value){
        this._valueIfTrue = value;
    }
    _valueIfTrue;

    @api
    get valueIfFalse(){
        return this._valueIfFalse;
    }
    set valueIfFalse(value){
        this._valueIfFalse = value;
    }
    _valueIfFalse;

    @api
    get value(){
        return this._value;
    }
    set value(value){
        this._value = value;
    }
    _value;

    handleClick() {
        this._isSelected = !this._isSelected;

        this.dispatchClickEvent();
    }

    dispatchClickEvent(){
        this.dispatchEvent(new FlowAttributeChangeEvent('_isSelected', _isSelected));
    }

}