The tab is going to display for businesses that have used GMB to publish their posts.
To be noted that all businesses having a GMB page don’t use posts feature and thus “Posts” won’t be found in all local business searches.
Maybe the increased visibility offered by Google search results will be a reward for more businesses to start posting to GMB.
See this example-
Users after tapping on the tab can go through the posts vertically, and a carousel of images at the top can be seen horizontally.
Google started providing insights for GMB posts earlier this month.
These insights show a number of clicks, views and the performance of metrics over a period of time.
Users publishing GMB posts should check their insights to assess if the new tab in the search results made an evident impact on views and clicks.