StargateJourney has structures that can generate only once per dimension and rely on their expected position (must be able to locate them).
When Structure Essentials is present, those structures are either not generated or cannot be located.

I tried updating the config like this:
structureessentials.json
Extending search timeout, extending radius, disabling fast lookup, disabling biome compat...

But the result was the same - the structure could not be located.
Creating the world with the same seed without structure essentials will generate and locate the structure without issues (~1110 blocks away).

To be more specific:
StargateJourney generates a single structure sgjourney:stargate/milky_way/buried/buried_stargate with the tag #sgjourney:has_stargate in the overworld in configured area.
By default, this area is 64 chunks around the world center.

And it must be able to locate that structure later.
(This also applies to some other structures from StargateJourney that are generated in other dimensions)

You may also be interested in a similar issue with SparseStructures mod.
That causes structures to generate in different places, breaking the ability to locate them in the expected area.
However, with SparseStructures, it is possible to fix it using their config to exclude structures from StargateJourney.
At some point in the future, hopefully with datapacks too.
So maybe a similar system might be a possible solution here as well?
Still, I don't know which feature of StructureEssentials is causing the problem here.

Modloader and Minecraft Version

Forge 1.20.1
NeoForge 1.21.1

Debug log

NeoForge 1.21.1
world seed -6356503363197043243
cupboard-1.21-2.9
structureessentials-1.21.1-4.5
stargatejourney-1.21.1-0.6.36

https://mclo.gs/Zat7IIs
or file:
debug.log

Does downgrading Structure Essentials to 4.3 fix this issue for you? If so, may help the dev to troubleshoot the cause

Unfortunately no, the problem persists with Structure Essentials 4.3.

fixed in 4.6