Is there anything built into the WordPress core to enable me to get the relative path from the “permalink structure” option

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Is there anything built into the WordPress core to enable me to get the relative path from the “permalink structure” option

No, because it isn’t necessary, PHP provides this via parse_url. Using php -a we can launch an interactive PHP shell and test the code:

php > echo parse_url( 'http://example.com/iamapost/100', PHP_URL_PATH );
/iamapost/100
php >

If we read the PHP docs we see that it also handles query strings, etc, e.g.:

php > echo parse_url( 'http://example.com/iamapost/100?foo=bar#test', PHP_URL_PATH );
/iamapost/100
php >

Your problem is not retrieving the relative URL.

Your results do not contain the /100 because your permalinks do not contain it. Run echo get_permalink(); and it will become obvious. You are assuming that your permalinks contain the post ID. They do not.

Given that:

get_option('permalink_structure') === "/%postname%/%post_id%/";

Can the relative path be taken from this or any permalink structure set up on the permalink settings page – whatever that might be…

Yes, via get_permalink() and parse_url.

I decided to spin up a local site of WP v5.6.1, and gave it the permalink structure you used:

enter image description here

I then fired up wp shell and ran the code and got the expected results:

vagrant@vvv:/srv/www/wordpress-one/public_html$ wp shell
wp> echo parse_url(get_permalink(168), PHP_URL_PATH);
/test-2/168/
wp> echo get_option('permalink_structure');
/%postname%/%post_id%/
wp>