std::string comparison (check whether string begins with another string)

I would use compare method:

std::string s("xyzblahblah");
std::string t("xyz")

if (s.compare(0, t.length(), t) == 0)
{
// ok
}

Look to the Boost's String Algo library, that has a number of useful functions, such as starts_with, istart_with (case insensitive), etc. If you want to use only part of boost libraries in your project, then you can use bcp utility to copy only needed files

It seems that std::string::starts_with is inside C++20, meanwhile std::string::find can be used

std::string s1("xyzblahblah");
std::string s2("xyz")

if (s1.find(s2) == 0)
{
   // ok, s1 starts with s2
}

I feel I'm not fully understanding your question. It looks as though it should be trivial:

s[0]=='x' && s[1]=='y' && s[2]=='z'

This only looks at (at most) the first three characters. The generalisation for a string which is unknown at compile time would require you to replace the above with a loop:

// look for t at the start of s
for (int i=0; i<s.length(); i++)
{
  if (s[i]!=t[i])
    return false;
}