Come dice Alka l'errore sta in quel blocco di codice, praticamente stai cercando di applicare includes su un oggetto e non su un array.


ti riporto un esempio sperando di aver capito il tuo problema.

codice:
<!DOCTYPE html>
<html lang="en">

<head>
    <meta charset="UTF-8">
    <meta http-equiv="X-UA-Compatible" content="IE=edge">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <title>Document</title>
</head>

<body>
    <form id="formInserimentoStudenti">
        <input type="text" name="search-field" id="search-field">
        <button id="btn-filter">Cerca Studente</button>
        <br><br>
        <input type="text" name="nome" id="nome">
        <input type="text" name="cognome" id="cognome">
        <button id="btn-student" type="submit">Inserisci studente</button>

    </form>

    <table>
        <thead>
            <tr>
                <th>Nome</th>
                <th>Cognome</th>
            </tr>
        </thead>
        <tbody id="listaStudenti"></tbody>
    </table>
    
    <script>
        class Studente {
            constructor(nome, cognome) {
                this.nome = nome
                this.cognome = cognome
            }
        }

        const listaStudenti = []

        document.addEventListener('DOMContentLoaded', () => {
            const btnStudent = document.querySelector('#btn-student')
            const inputFilter = document.querySelector('#search-field')
            const btnFilter = document.querySelector('#btn-filter')
            const tbody = document.querySelector('#listaStudenti')
            const nomeStudente = document.querySelector('#nome')
            const cognomeStudente = document.querySelector('#cognome')

            btnStudent.addEventListener('click', (e) => {
                e.preventDefault()
                if (nomeStudente.value == '' || cognomeStudente.value == '') return
                listaStudenti.push(new Studente(nomeStudente.value, cognomeStudente.value))
                popolaTabella(listaStudenti)
                nomeStudente.value = ''
                cognomeStudente.value = ''
            })

            btnFilter.addEventListener('click', (e) => {
                e.preventDefault()
                const filteredList = listaStudenti.filter(obj => {
                    return inputFilter.value !== '' ? (obj.nome == inputFilter.value) : listaStudenti
                })
                popolaTabella(filteredList)
            })

            function popolaTabella(studenti) {
                let tbodyContent = ''

                for (let student of studenti) {
                    tbodyContent += `
                <tr>
                <td>${student.nome}</td>
                <td>${student.cognome}</td>
                </tr>
                `
                }
                tbody.innerHTML = tbodyContent
            }

        })

    </script>
</body>

</html>