refactor: Utilize single nemo check plugin

[evaline-ju]

Feature Description

#30 introduced the internal plugin with separate Plugin code, but this overlaps with the existing external plugin.

Proposed Solution

To utilize the existing plugin, we will keep the plugin mainly as an internal plugin and update the external plugin scripts/references to utilize the plugin logic. This will allow for updates like the tool response updates #32 that also call out to the nemo check server to be in one place. Config hooks should likely be added as well.

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Additional Context

No response