So yes if and unless are effectively expressions in the form of statements

They are not.

$ perl -c -e'my $x = if (f()) { g(); } else { h(); }'
syntax error at -e line 1, near "= if"
-e had compilation errors.

$ perl -e'my $x = unless (f()) { g(); } else { h(); }'
syntax error at -e line 1, near "= unless"
-e had compilation errors.
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if statements and unless statements are statements, not expressions.

if (w/o else) and (the always short-circuiting) and are supposed to do the same

They're not, and they don't.

$ perl -c -e'my $x = ( f() and g() );'
-e syntax OK

$ perl -c -e'my $x = ( if (f()) { g() } );'
syntax error at -e line 1, near "( if"
-e had compilation errors.
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-MO=Concise shows opcodes, not operators. An if statement and an and expression often (but not always) use the and opcode, but that doesn't tell you anything relevant to this conversation.

Would you say an if statement in C and a while statement in C are the same thing because they both use the same branch opcode?

In short, you are begging the question. You are presuming an if statement does the same as an and expression to conclude that an if<c> statement does the same as an <c>and expression.