High-precision EUV spectroscopy of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>s</mml:mi> <mml:mn>2</mml:mn> <mml:mi>p</mml:mi> <mml:mspace width="0.28em"/> </mml:mrow> <mml:mrow> <mml:mmultiscr

High-accuracy extreme ultraviolet (EUV) spectroscopy of the $1{s}^{2}\phantom{\rule{0.16em}{0ex}}2s2p\phantom{\rule{0.28em}{0ex}} ^{1}P_{1}\text{\ensuremath{-}}1{s}^{2}2{s}^{2} ^{1}S_{0}$ electric dipole ($E1$) transitions in beryllium-like ${\mathrm{S}}^{12+}$ and $\mathrm{C}{\mathrm{l}}^{13+}$ was performed at the Shanghai High-Temperature Superconducting Electron Beam Ion Trap. Utilizing a portable high-resolution soft x-ray and EUV spectrometer, the measured $E1$ transition wavelengths for ${\mathrm{S}}^{12+}$ and $\mathrm{C}{\mathrm{l}}^{13+}$ were determined to be $256.6852(53)\phantom{\rule{0.16em}{0ex}}\AA{}$ and $237.8037(62)\phantom{\rule{0.16em}{0ex}}\AA{}$ (in vacuum), achieving relative uncertainties of 21 ppm and 26 ppm, respectively. Furthermore, the $E1$ transition energies for these ions were evaluated with ultra-high precision within an ab initio quantum electrodynamics (QED) framework to enable a stringent comparison with the experimental data. The measured values are in good agreement with the theoretical predictions, providing a precision test of QED and correlation effects in few-electron highly charged ions.