Flying machines are destroyed after a restart

Expected behavior

When saving the world, running flying machines are saved correctly.
After the world is loaded, the flying machines continue their movement.

Observed/Actual behavior

When saving or loading the world, it happens that the constructions are torn apart or do not continue their movement. It has also been reported that they have duplicated. We have not been able to reproduce this so far.

It is observed after the update from 1.19.2 to 1.19.4.

Steps/models to reproduce

@kennytv Has a server with a world to reproduce.

Steps to reproduce:

1. Start server and enter.
2. Activate flying machines via noteblocks.
3. Leave server
4. Restart server
5. Enter server again

Expectations:
After 5: Flying machines continue their movement.

Plugin and Datapack List

Paper version

[13:51:19 INFO]: fThis server is running Paper version git-Paper-538 (MC: 1.19.4) (Implementing API version 1.19.4-R0.1-SNAPSHOT) (Git: bcd8dc2)r
aYou are running the latest versionr
7oPrevious version: git-Paper-530 (MC: 1.19.4)

Other

No response

Start with the Paper 1.19.4 server and reproducible world mentioned in the issue, following the five listed steps around a flying machine activated by noteblocks. Compare the machine state before saving and after restarting; done means flying machines are neither destroyed nor duplicated and continue moving after the world loads.