BlockEntities won't update in all Cases.
Bug found with two shadow items set in a hopper (chest ...). Only on one item (always the latest you put into the Storage) will be updated.

.

are you using lithium while testing?

Yes, without it it functions. Is there a way to run nevertheless lithium?

yes, in the config folder there is a file called "lithium.properties"
in it you can disable "hopper optimizations" that are the cause of the incompatibility.

like this:

# This is the configuration file for Lithium.
#
# You can find information on editing this file and all the available options here:
# https://github.com/jellysquid3/lithium-fabric/wiki/Configuration-File
#
# By default, this file will be empty except for this notice.
mixin.block.hopper = false

In fact lithium of version 1.18+ has fixed the problem, you could cherry-pick the commit 33f485 and a82bc4 from latest branches to the 1.17- branch(To be more specific, 1.17 only as the hopper optimization is added in 1.17). It works well with carpet-shadow.

Perhaps carpet-shadow could also give a fix for it?