There is a bug in my project where the Gantt chart tooltip often gets stuck on the page and continues to display even when switching to other pages.

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Hello,
I suppose, you are not using the Gantt Instance approach.

If you use Gantt in Angular, React, Vue, or other framework related to node.js, it is expected to use the Gantt Instance approach.

When you open a page/tab/view with Gantt, you need to create a new Gantt instance. When you switch to a different page/tab/view, you need to destroy the Gantt instance:
https://docs.dhtmlx.com/gantt/desktop__multiple_gantts.html#destructorofganttanddataprocessorinstances

When Gantt is destroyed, the tooltip and popups are removed.
You can check how it works in the following demos:

https://files.dhtmlx.com/30d/f9efce5ac2b5298cb456fff8279fc78d/angular16+GanttInstance.zip

https://files.dhtmlx.com/30d/02b5b29ed6e3ee813e4a222d6a024a16/reactive-gantt+gantt-instance+7.0.13-trial.zip

https://files.dhtmlx.com/30d/4f25d33cbc4b19057f40a028577f9410/vue3+gantt-instance+trial_7.1.12.zip

Alternatively, you need to manually reset everything by yourself. And that includes manually removing the popups and tooltips.

The following article covers the known issues:
https://docs.dhtmlx.com/gantt/desktop__gantt_instance.html

Here are the demos where the tooltips and popups are not hidden:
https://files.dhtmlx.com/30d/284f415f444ae1ea1fdaf33314acae18/angular16+gantt_GPL.zip

https://files.dhtmlx.com/30d/ab90cf40072b2207de63ffc91e04047d/reactive-gantt+Gantt-instance-alternative.zip

https://files.dhtmlx.com/30d/ba3be5b2fbffd3484af6c2da06ba653e/vue3+gantt.zip

You will need to add this code when you switch to another tab to remove the DOM elements of the tooltips and popups:

      const popups = document.querySelectorAll(".gantt-info");
      popups.forEach(function(el){
        el.remove()
      })
      const tooltips = document.querySelectorAll(".gantt_tooltip");
      tooltips.forEach(function(el){
        el.remove()
      })

Here are the demos where it is fixed:

https://files.dhtmlx.com/30d/70dabbe7a7b74a5fe8c8aaa1488ea0ee/angular16+gantt_GPL.zip

https://files.dhtmlx.com/30d/5b56b486a60f5c6d1261202850331b4c/reactive-gantt+Gantt-instance-alternative.zip

https://files.dhtmlx.com/30d/c0a7cdde5ff4139e785733d9bfdbc9fb/vue3+gantt-gpl.zip