I looked at https://thebichirhandbook.com/
under "What's the next book" link that indicates a revised second edition is underway. Maybe that webpage needs correction?
Will the third print have additional changes? Adding new spawning comments to second print would make me regret buying the first print run.
The first print run sold out last year, so you would only be able to buy a second or thid print run of the first edition. No changes to the third run which I anticipate. The second edition is indeed being prepared (different cover illustration, lots of unused artwork), however this will not go to print for at least 10 years, or unless there are any substantial changes to their taxonomy (which to my knowledge, nobody is openly working on right now).
The bulk of our focus is on the next book in the handbook series.