Corresponde às quebras de linha em linhas que não começam com um caractere especial

const text = document.getElementById("x").innerText;
document.getElementById("x").innerText=text.replace(/(^[^@].*)(\r\n|\r|\n)/gm,"$1<BR/>")

#x { font-family: "Courier New", monospace;
  white-space: pre; }

<div id="x">@line 1: text text text 
line 2:
@line3: text text text
line 4: The line break after this text should be matched 
line 5: The line break after this text also should be selected 
line 6:
@line 7: this line break should not be selected
</div>