Plugin Internationalisation and textdomain

Yes, the text domain should be used.

PHP

The WordPress Documentation you referenced says:

The text domain is the second argument that is used in the internationalization functions. The text domain is a unique identifier, allowing WordPress to distinguish between all of the loaded translations.

React

On the JavaScript (React) side, below the heading How to use i18n in JavaScript and above the text Common functions available on the Internationalization page of the WordPress Block Editor Handbook Documentation it says:

The second argument is the text domain which must match the text domain slug specified by your plugin.

Hard typed text domains

Text domains should be hard-typed, and should not be variables. At the bottom of the section titled “Add text domain to strings“, the documentation says:

The text domain should be passed as a string to the localization functions instead of a variable. It allows parsing tools to differentiate between text domains. Example of what not to do:
__( ‘Translate me.’ , $text_domain );

The user of the multi-language multi-site may already be implementing an approach to internationalisation that you could follow. Otherwise, there are several options available to give you some idea of where to start looking.

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