In these bug, there's 2 scenarios to reproduce this. Mods are the same: Mod Menu, EBE, Smooth Boot and FAPI. Fabric 0.14.21. Used resource pack is a cubecraft a38e408437a1f6927b67021465e429a50973d9f2.zip
First:
Default EBE configs. Force resource pack compat is off.

1. Join to any world (if you turn on resource pack in the main menu bug will not work)
2. Make sure the chests open state are rendered properly.
3. Turn on resource pack that I provided (or any that causes the same problem)
4. An open state chest will have the wrong texture.
5. Turn off rp, the problem will occur again, but with vanilla textures
6. Turn on/off force resource pack compat or smooth lightning for chests
7. Problem will solve, but if you off smooth lighing or force resource pack compat, problem will not appear.

Also a video showcase

https://drive.google.com/file/d/1YOgwokamMvToKJvCyaV33IIgq5g4w5tE/view?usp=sharing

Second:
Force resource pack compat on before installing rp, other configs are default.

1. Join to any world (if you turn on resource pack in the main menu bug will not work)
2. Make sure the chests open state are rendered properly.
3. Turn on resource pack that I provided (or any that causes the same problem)
4. An open state chest will have the wrong texture.
5. Turn off rp, the problem will occur again, but with vanilla textures
6. Turn off force resource pack compat, problem will solve.
7. If you enable rp again, problem will occur again, but small chest texture will dissapear completely, cause one texture dissapear
8. If you enable force resource pack compat, problem will solve (what)
9. Off rp. Problem will not occur.

Video showcase

https://drive.google.com/file/d/1Hfd60mm7pm37oUUqK6-XqGxbEKebJZUm/view?usp=sharing

Sorry for my maybe bad eng, you can ask me any questions of this bug.

I'm getting this issue too. I am using Fabulously Optimized with a Vanilla Tweaks resource pack

So, some additional info:
If you join and quit cubecraft without smooth lightning on chests and "shulkerboxes?" on, they'll be broken.
But if you turn it on, it will be broken on cubecraft, but after quit everything will be fine.
Interesting

This still occurs in the latest version.
Game Version: 1.20.6
Mod List:

• Fabric API 0.100.0+1.20.6
• Mod Menu 10.0.0-beta.1
• Enhanced Block Entities 0.10+1.20.6

Completely new instance in Prism Launcher with everything on default settings.

Video Demonstration: https://youtu.be/KXo-QT6DcjI

Steps to reproduce:

1. Enable the resource pack for chest lids to become broken
2. Change mod configs to fix it (enable/disable enhanced chests)
3. Disable the resource pack to break chests again
4. Change mod config again to fix it

Resource Pack (texture pack) used:
https://vanillatweaks.net/picker/resource-packs/
Utility -> Visual Sapling Growth

Additional note: It's annoying having to disable/enable the mod every time I add/remove some random resource pack that breaks it, if a simple config reload could be added when a resource pack change is detected, that would be appriciated.