1. Don't put sessions in localstorage, use a cookie with the Secure and HttpOnly settings. They are then inaccessible to JavaScript.
2. Add a Content Security Policy to your headers. Start very tight i.e. default-src 'none'; style-src 'self'; img-src 'self'.
There's a really great PenTest checklist here https://pentestbook.six2dez.com/others/web-checklist So you can see it from the attackers perspective.