> My Search regex is a multiline regex (it contains multiple newlines).

I know, but when I copy it and paste it in any text editor (not just in the search field of EmEditor), it shows as a single line

also, have you noted that the original text is:
34,George,Clooney,3456346,LDL,356,mg
34,George,Clooney,3456346,HDL,324,ml
34,George,Clooney,3456346,VLDL,635,kg
34,Tom,Cruise,4573456,LDL,463,dl
34,Tom,Cruise,4573456,HDL,746,cm
34,Tom,Cruise,4573456,VLDL,435,dc
35,Al,Pacino,5646464,LDL,467,hg
35,Al,Pacino,5646464,HDL,352,df
35,Al,Pacino,5646464,VLDL,643,rf

and not just:
34,George,Clooney,3456346,LDL,356,mg
34,George,Clooney,3456346,HDL,324,ml
34,George,Clooney,3456346,VLDL,635,kg

isn't there any problem with that?