Rename framework/ to diachron/ and update all references

Update paths in .gitignore, cmd, develop, mgmt, sync.sh, check.sh,
fixup.sh, CLAUDE.md, docs/new-project.md, and backend/*.sh scripts.

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

.gitignore

@@ -1,5 +1,5 @@
 **/node_modules
-framework/downloads
-framework/binaries
-framework/.nodejs
-framework/.nodejs-config
+diachron/downloads
+diachron/binaries
+diachron/.nodejs
+diachron/.nodejs-config