infra: cleanup docs build (#21134)

Refactors the docs build in order to:
- run the same `make build` command in both vercel and local build
- incrementally build artifacts in 2 distinct steps, instead of building
all docs in-place (in vercel) or in a _dist dir (locally)

Highlights:
- introduces `make build` in order to build the docs
- collects and generates all files for the build in
`docs/build/intermediate`
- renders those jupyter notebook + markdown files into
`docs/build/outputs`

And now the outputs to host are in `docs/build/outputs`, which will need
a vercel settings change.

Todo:
- [ ] figure out how to point the right directory (right now deleting
and moving docs dir in vercel_build.sh isn't great)

Makefile

@@ -17,16 +17,11 @@ clean: docs_clean api_docs_clean
 
 ## docs_build: Build the documentation.
 docs_build:
-	docs/.local_build.sh
+	cd docs && make build-local
 
 ## docs_clean: Clean the documentation build artifacts.
 docs_clean:
-	@if [ -d _dist ]; then \
-		rm -r _dist; \
-		echo "Directory _dist has been cleaned."; \
-	else \
-		echo "Nothing to clean."; \
-	fi
+	cd docs && make clean
 
 ## docs_linkcheck: Run linkchecker on the documentation.
 docs_linkcheck: