marker not part of URL

I am not sure I understand the problem. When I click on your link, I get a map with a blue marker in the centre.

Ah indeed...

There is something strange happening: I bookmarked such a link and when opening the bookmark the marker does not appear, that's what makes me wonder whether someone else would see the marker - when you look at the URL there is no information of a possible marker, only a lat/long.

Also, when opening the Share panel, the marker can be shown/hidden just by (un)checking "Include marker", which makes me suspect that users with an OSM account could see a different behaviour from users without an account (and just receive the URL).

Here is another example: https://www.openstreetmap.org/#map=19/51.02877/3.71016&layers=C - this is the URL in a bookmark; the marker does not show up. When I enable the "Include marker" checkbox, all these bookmarks now show the marker. As far as I know, that checkbox is not set by default, so I wonder if a user without an OSM account will see the marker (even if that's the purpose of the checkbox).

Here is another example: in this URL I did not activate the marker option: https://www.openstreetmap.org/#map=19/51.02899/3.71075&layers=C as far as I can see , there is NO difference in the URL and I bet you will see the bookmark although I did not enable it.

I was about to say that, your last two examples do not show any marker for me as they do not include mlat and mlon, unlike the first one you posted. As far as I know it does not matter if you have an OSM account or are logged in.