In an Animation export the Gantt Chart is a static view by default, unless you apply a dynamic task filter. If you want the Gantt chart to adjust along with your animation, you can set a Look ahead Task Filter (Navigator>Task and Path Filters) so that as the Focus Time moves through the animation, the Task List will update accordingly. Make sure this Task Filter is active before you export your Animation.
There are 2 ways to do this:
Option A: Look ahead filter - This will show tasks that are active as of the Focus Time plus any future tasks within a given time length (e.g. 1d or 7d)
Option B: Date Range Filter - This can be used to show tasks in the recent past as well as tasks in the future. This option is probably only useful when the schedule contains few simultaneous tasks or is filtered to show only a subset of tasks (e.g. by work package, crew, or zone), otherwise, there may be too many tasks to fit into the Gantt window in the animation export.
The Gantt chart scrolls horizontally only in the animation (the Gantt Chart will not scroll vertically). Using a filter as described above to shows only active tasks can potentially reduce the task list so that all tasks can be seen in the vertical space allotted in the animation (so no vertical scrolling is necessary).
If after applying the 1d Look Ahead filter, there are still too many tasks to fit the Gantt Chart space in the animation, consider applying a second filter and combining it with the Look Ahead filter using the Task filters Operation: AND