When I place an enchanting table, I cannot retrieve it. It just disappear when I break it whatever the tool I use.
I play on a custom 1.16.4 modpack server but only quark odditties change enchanting tables. I've tried it, either on the server and solo world, it always disappear.
Here is the list of mods I use :

Abnormals Core
Alex's Mobs
AppleSkin
Applied Energistics 2
AutoRegLib
Botania
Charm
Citadel
Clumps
ComputerCraft(CC:T)
Controlling
Create
Curios API
Dungeon Crawl
Dungeons Plus
Dynamic Surroundings
Fishing Real
FTB Backups
GraveStone Mod
Guard Villagers
Here's What You're Looking At
Hunter illager
Inventory Sorter
JEI
JEI Integration
Morpheus(server only)
optifine (client side)
Patchouli
Practical tools
quark
Quark Oddities
Regrowth
Spawner Bug Fix
Spiders 2.0
Structure gel
The Conjurer
The Endergetic Expansion
Towers Of The Wild
Valhelsia Structures
Waila harvestability
Waystones
Xaero's Minimap
Xaero's World Map
YUNG's API
YUNG's Better Caves
YUNG's Better Mineshaft