but now in WordPress 6.0, there is no such attribute that exists in Gutenberg to select a new page template.
This is not true! WP 6.0 did not remove this functionality. In fact in the block editor it is even more prominent and has its own dedicated panel if you scroll up the sidebar:
If this isn’t showing then you should enable it in the block editor settings window:
Keep in mind that the article you’ve linked to is talking about the classic editor.
The final possibility, is that poor/strange formatting has broken the ability to parse your template header.
E.g. instead of this:
<?php
/*
* Template Name : Amaizing Inner Page 1 Template from me*
Do this:
<?php
/**
* Template Name: Amazing Inner Page 1 Template from me*
See the official documentation for page templates for details and examples: