What is the way to ship read-me strings like plugin-strings for internationalization?

You can ship translations of some of the metadata used in your main plugin file’s header comment fields. Namely: Name, Description, PluginURI, Author, and AuthorURI.

Just add the source strings into your PO/POT files exactly as they appear in your plugin headers. When a MO file is available containing these strings, WordPress will display the translations on the plugin activation/listing screens.

e.g. POT entry:

#. Name of the plugin
msgid "My Awesome plugin"
msgstr ""

If you want to translate the entire readme.txt file, then as already mentioned in the comments – you can’t. That file is only translated on wordpress.org when localised by the Glotpress team.

Note that the modal/popup that opens from the “View details” link on the plugins page is hosted on wordpress.org, so the latter applies.