The native upload endpoint accepts multipart form data for a running session. Each file must be at most 512 KiB, with at most 16 files per session. The Cloudflare Containers transport currently refuses this capability.
curl -X POST "https://api.tooluse.net/v1/browsers/sessions/$SESSION_ID/uploads" \
-H "Authorization: Bearer $TOOLUSE_API_KEY" \
-F "file=@./example.txt"
The response contains remotePath. Use that remote path with the file-input operation of your CDP automation client; a path on your own computer is not a remote path. Uploaded files are ephemeral and removed when the session ends.