Heart of Oak's specialization is to counter Regrow properties, specifically stripping off Regrow properties to fill this role. Most Druids with this upgrade can be used to deal with spaced Regrows, but Druids that also have Path 1 upgrades can be used to effectively counter grouped Regrows.
There is a certain Monkey Knowledge upgrade named Warm Oak that reduces the price of this upgrade by $100. Note that this applies after difficulty price multipliers.
The same Monkey Knowledge can be used to make it easier to farm with Jungle's Bounty Druids.
Heart of Oak is largely useless on Path 3 Druids due to possessing little pierce to compensate its high attack speed, rendering them less useful at stopping Regrows.
If utilizing the degrowth properties of Heart of Oak, add Heart of Thunder as a crosspath, to allow the high-pierce lightning bolts to strip off Regrow Bloon properties.
Adjusted to make crosspathing more important and worthy with Heart of Oak.
Heart of Oak now allows all attacks to degrow Regrow Bloons, not just thorns.
Heart of Oak no longer removes Regrow from bloons not damaged.
Heart of Oak upgrade icon in upgrades menu
Crosspathing in BTD6 (Top: Path 1, Bottom: Path 3)
Coincidentally, all of these upgrades come from Magic Monkeys as the 2nd upgrade of their 2nd path (Druid, Ninja, Alchemist, in the respective order).
Version 18.0 added a secret undocumented buff that allows all attacks including thorns to degrow Regrow Bloons. The description was changed from "Thorns convert Regrow Bloons into normal Bloons." to the current description to accomodate these changes.
This change has also made the 2TC combo Superstorm + Sky Shredder possible, which allows Round 61 to be possible with just a 3-2-0 Druid. This was shown on the official r/btd6 subreddit. Link.
This buff was not at all mentioned in the Version 18.0 patch notes. It was, however, officially mentioned in the Version 19.0 patch notes.
There was a challenge in the Advanced Challenges of Daily Challenges that showcased the Heart of Oak's on-hit de-Regrow property prior to the Version 22.0 nerf that no longer allows this interaction.
This, along with Heart of Thunder and Heart of Vengeance, all have the word "Heart" in it.
Even though the upgrade portrait shows the druid holding a shield in his right hand, a 0-2-0 druid (along with all 0-2-x druids, excluding 0-2-5) will hold the shield in the left hand.