If you have Review alt text before publishing turned on in App settings, generated alt text waits for you on the Review alt text page in the left menu.
Open it, tick the rows you want, and click Approve & publish. Each row also has an editable field, so you can fix the wording before approving, and a Remove button to reject a suggestion you do not want.
If you do not see a Review alt text link in the menu, that setting is off — which means alt text is being published automatically and there is nothing to approve.
Check the button label first. With rows ticked it shows a count, like Approve & publish (1). With nothing ticked it reads Approve & publish all and approves every suggestion in your store — ignoring what is on screen and ignoring your search. If you only want some images published, make sure the button shows a number.