While under the effects of the Amphibious Enchantment, Mantis Shrimp will be prevented from taking dry-out damage, but will still undergo the effects of drying out, namely, slowing to a crawl when on land without a Water Bucket, eventually coming to a standstill and being unable to be commanded. Additionally, they will also move at abnormally fast speeds through water.

The attached video demonstrates this (although for time reasons it does not show a Mantis Shrimp slowed to the point of standstill), with a tamed Mimic Octopus and Axolotl with Amphibious enchantments to demonstrate that they do not seem to undergo any additional speed penalties on land.

This may be intentional, as Amphibious may be intended to prevent dry-out damage and nothing more, but seeing as it allows land mobs to move through water, it's possible it's intended to allow aquatic mobs to move on land normally.

Minecraft version - 1.19.2
FML version - 43.1.53
Citadel version - 2.1.0
Alex's Mobs version - 1.21.0
Domestication Innovation version - 1.6.0