I found the cause and a temporary workaround for the issue.
The cause: when crafting iron nuggets from an iron ingot, you obtain AgriCraft's iron nuggets. Any recipe using iron nuggets will not work when using the ones from this mod - not even turning these 9 nuggets back into an iron ingot. The crafting recipes probably fail because they don't recognise these nuggets as valid ingredients. Using other mods' iron nuggets however works fine - I can now craft the OpenComputers components that I require.
The workaround: The server likes to replace any kind of iron nuggets with AgriCraft's version, even when the recipe says you will get, let's say, TechReborn's nuggets. Because of this, we need a way to obtain another mod's nuggets (and no, the Forge book doesn't work in this case). My solution was to smelt the bad nuggets in a Tinker's Construct smeltery and recast them into nugget molds to obtain TechReborn's iron nuggets. Using these I can now craft all of the recipes that need iron nuggets. Alternatively, a spawn shop that trades different mod types' nuggets in a 1 to 1 would work too (in fact that would be better), but hopefully not required if this issue gets resolved, because...
Additional notes: this problem only seems to occur on the Modded Minecraft Club FTB Beyond server. I haven't tried on any other public servers, but I have tried downloading the server files via the legacy FTB launcher and hosting my own local server, on which I was able to use the "bad" nuggets to successfully craft the aforementioned OpenComputers components.
I'm clueless as to why it won't work on this server, but I hope it gets resolved soon. This has been preventing me from progressing in my base for almost a week now.