Hi @Raki ,
Why don't you let the external users go to the library and upload documents there directly? This is much easier.
To develop such app with the UI in modern page, you may need to use SharePoint Framework to build your own web part.
In spfx, you can use PnP/PnPjs to upload files to library: https://pnp.github.io/pnpjs/sp/files/#adding-files
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