What documentation should I ask before I quit from a fully remote job?

Have the full record of all the communications related to leaving the job, preferably in writing. Even if you confirmed everything over a zoom call, send them an email from your personal account asking for a confirmation. This leaves no room for ambiguity.

Depending on your and their location there may be a double-taxation agreement between the countries, so check if you have the full tax record on your wages.

Check if you have a copy of your contract, NDA and Non-Compete.

Ask for a permission to publicly reference your work / contribution, if the NDA is too restrictive.