The bug

The visual indicator used to state the world is currently being saved is different across editions: Java Edition uses the text "Saving world", whereas Bedrock Edition uses an animation with a chest.

As the indicator was reintroduced to Java Edition in 1.18 after being absent since 1.2.5 (MC-73300), this should count as a valid parity issue.

How to fix

Add Bedrock Edition's saving world sprite to Java Edition.

Further notes

It may be a good idea to have this as a toggle, as to permit switching between the two different types of saving indicator, much like how the attack indicator can be toggled between the crosshair and hotbar versions.