Google has noted that the Search Generative Experience as a labs experiment runs through the end of this year, through December 2023. If you go to labs.google.com, you might see it yourself.

Here is a screenshot:

I assume before then it might have started to be released in the main Google.com search results. I have no clue how long this experiment will be labeled as an experiment and how long it will take Google to bring it to the main results.

But Google did label this one as ending in December 2023, so that does give us a clue.

Forum discussion at Twitter.