Google Sheets

Wasted too much on time on this because I assumed there weren't different directories with the same name. But eventually managed to get a one formula solution for both parts.

=sortn(lambda(f,query(if({1,-1}*f>{1e5,4e7-1-sum(--regexextract(A1,substitute
(regexreplace(A1,"(\d+)","($1)"),"$","\$")))},,f),"select sum(Col1), min(Col2)"))
(lambda(l,byrow(--regexextract(l,regexreplace(l,"(\d+)","($1)")),lambda(r,sum(r))))
(lambda(e,g,byrow(regexreplace(regexreplace(g,"dir (\w+)","dir "&e&"/$1"),"/+","/"),
lambda(r,reduce(r&char(10),e,lambda(a,c,ifna(regexreplace(regexreplace(a,
regexextract(a,"(?ms)dir "&c&"\n"),filter(g,e=regexextract(a,
"(?ms)dir ("&c&")\n"))&char(10)),"dir (\w+)","dir "&c&"/$1"),a))))))
(query(unique(scan(,flatten(regexextract(A1&char(10)&"$",substitute(
regexreplace(A1&char(10)&"$","(?ms)cd ([^/]+?)(\n\$)","cd ($1)$2"),"$","\$"))),
lambda(a,c,if(c<>"..",a&"/"&c,regexextract(a,"(.*)/"))))),"where Col1 is not null"),
flatten(regexextract(A1&char(10)&"$",substitute(regexreplace(A1&char(10)&"$",
"(?ms)(cd \w+\n\$ ls\n)(.*?)(\n\$)","$1($2)$3"),"$","\$")))))))

This formula will spill one cell to the right with the result of part2 and it assumes that the whole input is in cell A1.