no widget for new plugin

there is no widget available to be used.

correct.

documentation:
https://plugins.twinpictures.de/plugins/t-minus-countdown/documentation/

that is the link for the jQuery plugin and still indicates a widget. Last updated 2017.

This plugin, jQuery T(-) Countdown Widget, does have a sidebar widget, and the documentation as linked to above.

The new plugin, T(-) Countdown does not currently and will not ever have a classic sidebar widget, as WordPress is shifting from widgets to Gutenberg Blocks. The new plugin will offer a Gutenberg block (available now as a release candidate on GitHub).

There is new documentation coming, but in the meantime, the shortcode documentation is valid for both plugins.

Use the old version for now, but soon WordPress will migrate away from using classic plugins. When that time comes, the new plugin will pick up and continue where the old one retired.

Hope this clears things up.