To zoom in to a feature in a Map Widget, the action has to be triggered from another Widget, such as List Widget. Feature Info is also capable of triggering actions. You have to set up these actions under Message Action, not Data Action. However, I don't believe you you will be able to zoom in to a point just by clicking on it, since you can't send a Message Action to the same Widget that triggered it. But we can work around this.
ESRI should come up with a more elegant solution (if there is one I don't know), but to acomplish this behaviour you should:
1. Create a new webmap that contains only the layer you are trying to select (e.g. points layer), remove basemap;
2. Add a second Map Widget (Map2) to your Experience (anywhere) and connect it to your new webmap;
3. Select your first Map Widget and add an Action to it this way:
a) Add a trigger;
b) Record selection changes
c) Widgets/Map 2
d) Zoom to
e) Select data - Select the point layer within the main Map Widget.
4. Select your second Map Widget (Map 2) and add an Action to it like this:
a) Add a trigger;
b) Extent changes;
c) Widgets/Map
d) Zoom to
5. Try it out and see if when you select a point, the map will zoom to it. It might not work at first, if it doesn't save and refresh the page.
Let me know if you end up trying this.