In all cases, make sure you are not exposing your keys or endpoints where other people could use your keys to access your personal account.
If you learn OAuth and CORS, you might be able to write an axios or fetch client. Node's "request" module is not easy to reverse engineer into client-side JS code. The browser versions I've seen don't support the OAuth addon it uses.
If you deploy to now.sh or a VPS, or write an Electron desktop client, you could use the node, golang, or python clients in the backend to proxy tumblr requests.
If you deploy to netlify, you could use the node or golang netlify functions to proxy tumblr requests.
If you deploy to any VPS environment or use serverless/lambda/cloudfunctions, you could proxy tumblr requests in most of the available cloud libraries.
I suspect you could compile the golang or c client to webassembly and expose their functions to JavaScript, but I don't recommend trying this.