Description of the issue:

Two groups of things that are a problem related to seeds and vegetables in the cloche.
Group one: potatoes and carrots - can be put in the cloche but don't grow - might be a problem with my setup (either in Minecraft or mods I have installed - e.g. Pam's Harvestcraft)

Group two: beetroot and possibly wheat / barley / barley - beetroot and beetroot seeds (vanilla), wheat (Pam's Harvestcraft is the ultimate override I think), barley (Natura), barley (Pam's Harvestcraft) - the barleys don't override each other - none of these can be put in the cloche at all; I'm presuming mod interaction in the case of everything but the beetroot which is vanilla minecraft, so I guess it's not supported yet?

May be related to issue 2882:
#2882

Versions & Modlist:

Forge: forge1.12.2-14.23.2.2611
ImmersiveEngineering: 0.12-78
Pam'sHarvestCraft: 1.12.2q
Hatchery: 1.12.2-2.1.2
CookingForBlockheads:1.12.1-6.3.17
Natura:1.12.2-4.3.2.42

(I can add a full mod list if that would be helpful but it's a relatively light modpack with nothing else related to food).

Mod list:

Mods that do stuff to Minecraft internals and add items / entities / blocks:
Baubles-1.12-1.5.2.jar
BiomesOPlenty-1.12.2-7.0.1.2309-universal.jar
Botania+r1.10-353.jar
chickens-6.0.4.jar
CookingForBlockheads_1.12.1-6.3.17.jar
ImmersiveEngineering-0.12-78-core.jar
ImmersiveEngineering-0.12-78.jar
journeymap-1.12.2-5.5.2.jar
natura-1.12.2-4.3.2.42.jar
Pam's+HarvestCraft+1.12.2q.jar
StorageDrawers-1.12.2-5.3.5.jar

Mods that do stuff to Minecraft internals:
AIImprovements-1.12-0.0.1b3.jar
autoplant-1.12-1.0.0.jar
Chameleon-1.12-4.1.3.jar
Hwyla-1.8.23-B38_1.12.jar
JEHC-1.12.2-1.4.1.0.jar
jei_1.12.2-4.8.5.147.jar
jeiintegration_1.12.2-1.5.1.36.jar
Mantle-1.12-1.3.1.21.jar
OptiFine_1.12.2_HD_U_C9.jar
TreeChopper-1.12.2-1.2.4.jar
WailaHarvestability-mc1.12-1.1.12.jar

Mods that add items / entities / blocks:
chameleoncreepers-1.4.1-1.12.jar
hatchery-1.12.2-2.1.2.jar
japaricraftmod-1.12.2-3.8.8.jar
morechickens-1.12.2-3.1.0.jar
OpenGlider-1.12.1-1.1.0.jar
Owls-1.12.2-1.0.1.jar
Pam's+Llama+Milking+1.12.2b.jar
Pam's+Pig+Skin+1.12.2b.jar
Pam's+Sheep+Milking+1.12.2b.jar
Pam's+Squid+Milking+1.12.2a.jar
simplytea-1.4.jar
Waddles-1.12.2-0.5.6.jar

P.S. All mods at latest version last week and there are only a couple that produce even warnings - reported. though a couple have (of course) some bugs outstanding (Pam's Harvestcraft, for example).

Hatchery has a liquid_fertilizer liquid registered here:
/src/main/java/com/gendeathrow/hatchery/fluid/LiquidFertilizer.java
as well as fertilized_dirt and _farmland blocks here and here:
/src/main/java/com/gendeathrow/hatchery/block/fertilizedDirt/FertilizedDirt.java
/src/main/java/com/gendeathrow/hatchery/block/fertilizedDirt/FertilizedFarmland.java

Immersive Engineering seems to search for OreDictionary entries for fertilizer items here:
/src/main/java/blusunrize/immersiveengineering/api/tool/BelljarHandler.java - line 414

Is this potentially a problem?

(I don't know if "OreDictionary.itemMatches(bonemeal,fertilizer,true)" does substring matches or not and I'm out of time for the moment - apologies).

IE has no compatibility with Hatchery. Unless they add it, none of their fertilizer or dirt will work in the Cloche.
That's why you're supposed to test this with IE .-.

Hatchery doesn't add anything into IE for compatibility. I just tested this on my side, with same versions they are using. and the Garden Cloche worked as intended.

Edit: I only tested my mod with your mod.. nothing else

Well yeah exactly. It works fine when you use stuff actually designed to work with it, lol.
Given that I don't add Hatchery compat, that would be why it doesn't work (and that's also why you're supposed to provide screenshots).

Can't confirm on Barley, I'm pretty sure I added compat for all of Pam's stuff, but Beetroot works just fine for me:

Please attempt to reproduce the beetroot issue an a test instance with just IE, and if non-reproducable, attempt to identify the cross-mod interaction problem via binary search.

Suddenly realised that my cloche didn't have anything in the fertiliser column (this is my first time using one) and noticed it in your screenshot. This meant that I had to test Hatchery first since it has fertilised dirt so maybe it messed with more than I realised.
It appears that this is the case as with only IM and Hatchery installed nothing will grow in the cloche whether you use fertilised dirt or not. The fertiliser bar just sits at zero.

See Hatchery issue 146 here:
GenDeathrow/Hatchery#146

I'm not suggesting that there was any compat. stuff in place and I used vanilla stuff in the cloche - see below. This is still a problem - replacing the items does not fix it and moving every mod out of the way and starting an entirely new world does not fix it - you will note I used creative mode to test this because I am not willing to put in the days or work necessary to recreate this in a survival world because I already have a survival world it doesn't work in - one that is now blocked from moving forward at all due to this issue (maybe the problem is not with these mods but essentially I can't play this world unless I can fix this so I'm willing to put a lot of work into fixing this but I need help - that's why I'm here and spending a lot of time I barely have to get to the bottom of this - i.e. if there is anything I can do to help track this down ask and I'll do my best to do it).

Here is my setup recreated in a brand new world with only hatchery, IE and forge.

Note that the column next to the water level is empty - this should be full. Note I'm also only using a vanilla carrot and vanilla dirt.

What I was guessing was the problem is a name clash between things created in hatchery and things used in IE... however I have not read anything more than a few hundred lines of each code base so this is a guess based on experience rather than any real knowledge of either code base.

If you can show me your setup maybe I can put that together and confirm it's not a problem for me - maybe there is something to do with my setup (forge or minecraft) that is a problem I need to fix.

The lever you're using to activate your pump is also adjacent to your cloche, and the redstone signal is telling the cloche to suspend activity. Try with the lever on a different side of the pump.

^ what he said.