With Carpet's movableTileEntities & this mod's largeBarrels rules enabled, hoppers will continue to transfer items to large barrels after they are moved away.

Reproduced in Minecraft 1.19.4 & 1.19.2

Minnecraft 1.19.4

Carpet Mod - 1.4.101+v230219
Carpet TIS Addition - 1.46.1
Fabric API - 0.78.0+1.19.4
Lithium - 0.11.1
Mod Menu - 6.1.0-rc.4
No Telemetry - 1.7.0
Sodium - 0.4.10+build.24
Starlight - 1.1.1+fabric.ae22326

Minecraft 1.19.2

Carpet Mod - 1.4.84
Carpet TIS Addition - 1.44.0-bp.2
Fabric API - 0.76.0+1.19.2
Lithium - 0.11.1
Mod Menu - 4.2.0-beta.2
No Telemetry - 1.7.0
Sodium - 0.4.4+build.18
Starlight - 1.1.1+fabric.ae22326

It works properly without Lithium.

try remove lithium. its hopper optimization might be the cause

Try test with other inventory blocks, e.g. double chest, single barrel / chest, droppers. If the same issue occours, then it's caused by the incompatibility between carpet's movableBlockEntities rule and lithium, and I'll suggest to report this issue to lithium or carpet

Oops, you were right, this happens with chests, etc, without TIS Addition installed. I'll move this to the Carpet Mod repository.

gnembon/fabric-carpet#1704