I have downloaded the most recent release of Continuity (3.0.0+1.21.4) and put it in my mods folder but every time I go to launch Minecraft I get an incompatible mods crash telling me that my version is not compatible with Fabric Api and Sodium which I have downloaded at 1.21.4 as well - Can anyone tell me why this won't work?

Not without your game log.

Not without your game log.

Sorry how do I get that?

Is this what your looking for?

Incompatible mods found!
net.fabricmc.loader.impl.FormattedException: Some of your mods are incompatible with the game or each other!
A potential solution has been determined, this may resolve your problem:
- Replace mod 'Continuity' (continuity) 3.0.0+1.21.4 with any version that is compatible with:
- fabric-api 0.110.5+1.21.4
- sodium 0.6.2+mc1.21.4
More details:
- Mod 'Continuity' (continuity) 3.0.0+1.21.4 requires version 0.113.0 or later of mod 'Fabric API' (fabric-api), but only the wrong version is present: 0.110.5+1.21.4!
- Mod 'Continuity' (continuity) 3.0.0+1.21.4 is incompatible with any version before 0.6.6 of mod 'Sodium' (sodium), but a matching version is present: 0.6.2+mc1.21.4!
at net.fabricmc.loader.impl.FormattedException.ofLocalized(FormattedException.java:51)
at net.fabricmc.loader.impl.FabricLoaderImpl.load(FabricLoaderImpl.java:196)
at net.fabricmc.loader.impl.launch.knot.Knot.init(Knot.java:146)
at net.fabricmc.loader.impl.launch.knot.Knot.launch(Knot.java:68)
at net.fabricmc.loader.impl.launch.knot.KnotClient.main(KnotClient.java:23)

Yes, that works. Update Fabric API to at least 0.113.0 and Sodium to at least 0.6.6.