according to ngbtooltip doc https://ng-bootstrap.github.io/#/components/tooltip/api
isOpen
is a method and not an input/output
if you want to set a boolean when tooltip is open or not you can play with the two output hidden and shown
hidden : An event emitted when the tooltip closing animation has
finished. Contains no payload.
shown : An event emitted when the tooltip opening animation has
finished. Contains no payload.
in your code it can look like
<li class="mt-menu-icon-wrapper" placement="right" [ngbTooltip]="tooltip" triggers="manual"(mouseenter)="showTooltip('settings')" (mouseleave)="hideTooltip('settings')"
[closeDelay]="300" (shown)="tooltipDisplay(true)" (hidden)="tooltipDisplay(false)"></li>
in controller have a method
tooltipDisplay(isOpen:boolean) {
this.isOpenFlag = isOpen;
}