When right clicking on certain tinkers blocks which are not usable at the time of right clicking, the hand animation is still played, despite the fact no interaction actually took place.

As Mojang have been cracking down on cases of these in vanilla in 1.15 and 1.16, I'd also recommend removing these from the mod as well where they arise.

Examples:

• Seared faucet
• Casting table
• Casing basin
• Melter, with a bucket, when an insufficient amount of liquid is inside

• Minecraft: 1.16.5
• Forge: 36.1.0
• Mantle: 1.6.92
• Tinkers Construct: 3.0.2.96

Confirmed

Can it be reproduced with just Tinkers Construct? If not, list the other mods required to reproduce the issue.
Almost certaintly