When chasing the player or other mobs, the Bedrock Warden (despite its high HP) will not allow itself to fall more than 3 blocks. On Java Edition 1.19, the Warden was tested up to a 20-block fall and did not hesitate in order to chase down the player.

Steps to reproduce:
On Java Edition, create a random world in creative mode and build an 18-block pillar similar to the one in the following screenshot and summon a Warden on top of it:

Optionally, give yourself some Enchanted Apples to survive the Warden attacks while you make it angry. Then switch to survival mode and have the Warden chase you.

On Bedrock Edition, create a random world in creative mode and build a 3-block pillar similar to the one in the following screenshot and summon a Warden on top of it.

As seen in the image, the Warden will happily wander off the pillar.

Now, raise the pillar to 4 blocks high as seen in screenshot:

Again, optionally give yourself Enchanted Apples and switch to survivor mode and try to make the Warden chase you.

Expected Result:
As experienced in Java Edition, the Warden should fall and take damage in order to chase the player down. Note that the maximum height the Warden will fall on Java is unknown; 20 blocks was chosen as a practical height to test with since it is within range of its hearing.

Observed Result:
In Bedrock Edition, no matter how angry the Warden gets, it will never step off a 4 block or higher pillar in order to chase the player.