Bra-ket notation typefaces

As suggested in a comment, you can use DeclareMathDelimiter from mathtools to define bra and ket.

documentclass{article}
usepackage{mathtools}

DeclarePairedDelimiter{bra}{langle}{rvert}
DeclarePairedDelimiter{ket}{lvert}{rangle}

begin{document}
[ bra{x} ket{y} quad bra[big]{x}ket[big]{y^2}
]
end{document}

There is also a definition of braket as an example on page 28 of the mathtools manual.

DeclarePairedDelimiterXbraket[3]%
  {langle}%
  {rangle}%
  {#1,delimsizevert,mathopen{}#2,delimsizevert,mathopen{}#3}

The manual also has an example of setting three arguments within a bra, a ket and in between.

If you want to change the font used only for these delimiters, there is a standard interface for this in `unicode-math:

documentclass{article}
usepackage{mathtools}
usepackage{unicode-math}

setmathfont{NewCMMath-Book}
setmathfont{Libertinus Math}[
  Scale=MatchUppercase,
  range={langle,rangle,vert}]

DeclarePairedDelimiter{bra}{langle}{rvert}
DeclarePairedDelimiter{ket}{lvert}{rangle}

begin{document}
[ bra{x} ket{y} quad bra[big]{x}ket[big]{y^2}
]
end{document}

To redefine langlw, rangle, etc. with legacy math fonts is less standardized. It involves loading a symbol alphabet (of which you only have sixteen) and checking its font table.