A: Zed is one of the agents vexp auto-configures, so it works with your exact setup, no Claude or online tools needed. And since vexp is fully local with its own optional on-device model, your local stack is right where it belongs.
To be clear on the pieces: Zed handles the MCP connection to vexp and passes context to your model, LM Studio just serves the model. So the integration lives in Zed, not LM Studio. One thing that helps is using a local model that's decent at tool calling, since the agent needs to actually invoke vexp's tools, but that's on the model side, Zed does the wiring.
On your token issue: your intuition is right, that's exactly what vexp does, it keeps code out of context and loads only the slice that matters per request, so it cuts the code side of your bloat (usually the biggest part). It won't shrink the conversation history itself, that's what compacting handles, but the code is normally the heavy piece.
Free tier if you want to try it on Zed and see the drop live.