Seems that TG servers are escaping '_' in links by default, yet the library functions blindly replace it by '\ _'.

Try it out - 'https://site_name.com' becomes 'https: // site \ _name.com' after
msg.text_markdown_urled or
msg.caption_markdown_urled

Current tests miss exactly this case

Guess tomorrow I'll write and commit my solution, need this for work anyway. The simpliest one is to get final urled string and replace '_' by '_' inside the url clauses.