How small can a Product Hunt launch be?

https://help.producthunt.com/en/articles/484934-can-i-re-post-a-product-that-s-already-been-posted

We require at least 6 months in-between postings along with a significant update to the product for products that have previously been posted or are products from a company that has recently posted. Product updates must be substantial, such as the launch of a mobile app or complete product redesign with new functionality, to be considered for resubmission.

A huge version change is always required. If it's a small update, you might want inform your users instead of using it as a launch :)

Be careful with this - if they decide you don't fit the rules for "significant update" they will delist your update without any warning or explanation, leading to a very annoying day of emailing support and regretting asking all your friends to upvote the product earlier in the day.

Happened to me, really not fun.

Yeah you can relaunch as long as you can show product hunt there is a significant change in your product i.e. a new feature or integration as you said. People normally identify as '2.0,' etc.