why apex class is not calling from LWC.

Hi @Ayush Singhal

This is the updated Apex Code and Js and Html.

if this answer resolve your query please mark as helpful.

Thanks.

public with sharing class OpportunityHandler {
    @AuraEnabled(cacheable = true)
    public static List<Opportunity> getOpportunities(String StageName, Date CloseDate) {
        String query = 'SELECT Id, Name, CloseDate, StageName FROM Opportunity';
        Boolean whereClauseAdded = false;
        // Add filter for StageName if provided
        if (String.isNotBlank(StageName)) {
            query += ' WHERE StageName = :StageName';
            whereClauseAdded = true;
        }
        // Add filter for CloseDate if provided
        if (CloseDate != null) {
            if (whereClauseAdded) {
                query += ' AND CloseDate >= :CloseDate';
            } else {
                query += ' WHERE CloseDate >= :CloseDate';
                whereClauseAdded = true;
            }
        }
        // Execute query
        return Database.query(query);
    }
}
updated Js 
import { LightningElement, wire } from 'lwc';
import Opplist from '@salesforce/apex/OpportunityHandler.getOpportunities';
import { getObjectInfo, getPicklistValues } from 'lightning/uiObjectInfoApi';
import StageName from '@salesforce/schema/Opportunity.StageName';
export default class OppWebComponent extends LightningElement {
    opportunityData;
    CloseDate = null;
    StageName = '';
    error;
    options = [];
    // Wire to fetch opportunity data from Apex method
    @wire(Opplist, {
        StageName: '$StageName',
        CloseDate: '$CloseDate'
    })
    wiredOpportunities({ data, error }) {
        if (data) {
            this.opportunityData = data;
            this.error = undefined;
        } else if (error) {
            this.opportunityData = undefined;
            this.error = error;
        }
    }
    // Handle changes for CloseDate and StageName
    handleChange(event) {
        const { name, value } = event.target;
        if (name === 'stage') {
            this.StageName = value;
        } else if (name === 'date') {
            this.CloseDate = value;
        }
    }
    // Wire to fetch Object Info (Opportunity object info)
    @wire(getObjectInfo, { objectApiName: 'Opportunity' })  // Change 'Account' to 'Opportunity' for StageName field
    objectInfo;
    // Wire to fetch picklist values for StageName field
    @wire(getPicklistValues, {
        recordTypeId: '$objectInfo.data.defaultRecordTypeId',
        fieldApiName: StageName
    })
    wiredPicklist({ data, error }) {
        if (data) {
            this.options = data.values;
        } else if (error) {
            console.error('Error fetching picklist values: ', error);
        }
    }
}
Update Html
<template>
    <lightning-card title="Opportunity Filter">
        <lightning-combobox
            name="stage"
            label="Status"
            value={StageName}
            placeholder="Select Stage"
            options={options}
            onchange={handleChange}
        ></lightning-combobox>
        <lightning-input
            value={CloseDate}
            type="Date"
            name="date"
            onchange={handleChange}
        ></lightning-input>
    </lightning-card>
    <lightning-card title="Opportunity List">
        <template if:true={opportunityData}>
            <lightning-layout multiple-rows="true">
                <template for:each={opportunityData} for:item="opp">
                    <lightning-layout-item size="4" key={opp.Id}>
                        <c-opp-tile opportunity={opp}></c-opp-tile>
                    </lightning-layout-item>
                </template>
            </lightning-layout>
        </template>
    </lightning-card>
</template>