How to link current user to their author page through shortcodes

You’re trying to return a <?php block as text, which you don’t need to do, and is the wrong thing to do – it won’t get executed, even if you do return it correctly. Your specific syntax error is this bit:

function my_users_shortcode( $atts, $content) {
return '<?php
    if ( is_user_logged_in() ) {
        echo '<a href="' . home_url()

where you have the ' from the echo inside a string that you’re delimiting with 's too, and you can see from the syntax highlighting here that it thinks the string ends with echo ' and that the <a href is now PHP code again. If you did want to do that, you’d need to escape the 's with backslashes to make them part of the string and not the ends of the string, i.e.

return '<?php  echo \'a href="\' . home_url(); ?>';

But you don’t have to do that: since we’re currently running PHP code in the my_users_shortcode handler you can just echo the link from there, rather than trying to return a PHP snippet to try and execute later (which won’t work), i.e.

function my_users_shortcode( $atts, $content ) {
    if ( is_user_logged_in() ) {
        echo '<a href="' . home_url() . '/author/ ' .
             get_the_author_meta( 'user_login',  wp_get_current_user()->ID ) .
             '"> My personal page</a>';
    } else {
        echo '<a href="' . wp_login_url() . '" title="Login">Login</a>';
    }
}
add_shortcode( 'my_shortcode', 'my_users_shortcode' );

That said, as discussed in the comments I would use get_author_posts_url to generate the author page URL rather than trying to construct it yourself, and I think you ought to have some esc_urls too:

function my_users_shortcode( $atts, $content ) {
    if ( is_user_logged_in() ) {
        echo '<a href="' . esc_url( get_author_posts_url( wp_get_current_user()->ID ) ) .
             '">My personal page</a>';
    } else {
        echo '<a href="' . esc_url( wp_login_url() ) . '" title="Login">Login</a>';
    }
}
add_shortcode( 'my_shortcode', 'my_users_shortcode' );

(and if for the future you want the text to be translatable you need to wrap those parts in __('') too)