Ensure you have completely removed any versions of node you have. This is very important espciatlly if you have used brew to install. If you have downloaded the .pkg file from node.
Rosetta is going to interpret the x86_64 binaries to ARM so you'll need to install this.
softwareupdate --install-rosetta
I have taken the liberty of creating a gist that provides a bash script to install and link the instant client. If you don't want to use it you can follow the steps contained within the bash script.
In your shell config of choice add an alias to execute your package manager the arch software, to make it more convienent. Remember that if you do this all your node projects will be run this way which may have poorer performance. I'll use npm as an example since it's the entry point in my use case.
alias npm='arch -x86_64 npm'
Firstly make sure you remove the package-lock.json and the node_modules to ensure nothing is being reused.
npm install
Once the install is complete you'll know the instant client has been found if node-oracle does not complain about not finding the x86_64 binaries.
Now run the entry script
npm start
And just like that it should hopefully work for you.