Is it possible to have the "Sign Up" button persist during scroll, rather than the "Log In" one?

It is possible, here’s one way to do it.

You’re essentially replacing our default header-buttons widget and moving !attrs.topic. You can add this to a theme in the header section (admin > customize > themes > edit CSS/HTML).

<script type="text/discourse-plugin" version="0.8.13">
api.reopenWidget("header-buttons", {
      tagName: "span.header-buttons",

  html(attrs) {
    if (this.currentUser) {
      return;
    }

    const buttons = [];

    if (attrs.canSignUp) {
      buttons.push(
        this.attach("button", {
          label: "sign_up",
          className: "btn-primary btn-small sign-up-button",
          action: "showCreateAccount"
        })
      );
    }

    if (!attrs.topic) {
    buttons.push(
      this.attach("button", {
        label: "log_in",
        className: "btn-primary btn-small login-button",
        action: "showLogin",
        icon: "user"
      })
    );
    }
    
    return buttons;
  }
});
</script>