Correct me if i am wrong but even if we make the parent link of children collections we still are not able to get the child using an endpoint like below
{base_url}/collections/{parent_collections}/{child_collection} .
Couldn't it be made more natively ?

Hi. You are correct. To introduce a better way to crawl collections you would have to propose changes to the STAC api spec itself or maybe propose a new STAC extension that could add new routes to STAC apis like this one.

I see that there is a children extension alreadyhere - we would have to add support for something like this to sfeos

That seems useful however, i believe there should be a way to achieve that without having that extension because it is just a proposal and stac spec has been allowing collections having another collection as a child. Unfortunately i was not able to find a published, good example