Welcome to the community, @KonstantinKharitonov!
It’s a very strange limitation or bug in Airtable, but you can’t make the links clickable in an embedded view if the URLs are the primary field in the linked table.
The workaround for this is to create the links in a different URL field in the linked table (not the primary field), and then back in your main table, you will need to create a lookup field to lookup this new URL field.
This lookup field will work the way you want it to work. It will have clickable links in it.
I would also recommend emailing firstname.lastname@example.org to ask them to improve this feature in the way that you were expecting it to work.