I am an Indian citizen holding an Indian passport. I went to VFS to apply for a Schengen visa, and they noticed that the passport cover is coming off. I did not notice properly when they noticed if the binding is coming off or if it is just the cover coming off from the booklet. They did accept my application though. I am traveling to the US with a break in Europe for a week.
I am planning to get a re-issued passport using the Tatkal, but I am wondering if I should get the visas also stamped again in the new passport. As per the page here, the US embassy in Japan seems to suggest "If the photo page on your passport has been damaged (e.g. has become detached, or looks like it may become detached, from the rest of the passport), please apply for a new visa in a new passport, submitting both the damaged and new passport in support of your application." Do I need to apply for new visas and get them stamped in the passport?