Some random responses...

do you dispute that there is a left-curly (and a right-curly) in the \x{A3f4} string? What else would you call it/them?

I do not dispute that, so this string itself never represents a left curly brace, rather it has a left curly brace in it.

Oh, so you were thinking that "\x{A3f4}" when compiled double-quotishy into a string and then printed should print a left-curly! I follow you a little better now. My terminal is not configured for Unicode (as I assume this character to be) right now, so I cannot confirm what it will print, and I'm reluctant to launch myself into Unicode-land on-line to find out. However, I agree that the escape sequence \x{A3f4} when compiled double-quotishly (e.g., "ab\x{A3f4}cd") will compile to some character. But the single-quote-compiled string '\x{A3f4}' will always be literally \x{A3f4} and nothing else.

It's important to understand how backslashes (escapes) are compiled in single- and double-quoted strings. Consider the following:

Win8 Strawberry 5.8.9.5 (32)  Tue 06/07/2022 12:17:53
C:\@Work\Perl\monks
>perl

use strict;
use warnings;

print '-\-\\-\\\-\\\\-\\\\\-\\\\\\-\\\\\\\-\\\\\\\\-';

^Z
-\-\-\\-\\-\\\-\\\-\\\\-\\\\-
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Why do '\\\\\\\' and '\\\\\\\\' (7 and 8 backslashes, respectively) both compile to and print as four backslashes? How would this be different if compiled as a double-quoted string?

DB<1> $str2='\\x{263}'

This compiles to (and prints) the literal string \x{263} or literal-backslash, literal-lowercase-x, literal-left-curly, literal-2, literal-6, literal-3, literal-right-curly. The hex built-in cannot interpret a string in this format (and so returns zero (update: and a warning)), but can in "proper" format:

Win8 Strawberry 5.8.9.5 (32)  Tue 06/07/2022 22:09:02
C:\@Work\Perl\monks
>perl

use strict;
use warnings;

my $h1 = 'A3f4';
my $h2 = 'xA3f4';

print hex 'A3f4',  "\n";
print hex $h1,     "\n";
print hex 'xA3f4', "\n";
print hex $h2,     "\n";

print hex '\xA3f4',   "\n";
print hex '\x{A3f4}', "\n";

^Z
41972
41972
41972
41972
Illegal hexadecimal digit '\' ignored at - line 13.
0
Illegal hexadecimal digit '\' ignored at - line 14.
0
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    DB<10> $str4='\x{aF}'
...
How do I tease 175 out of $str4?

We know that \x{aF} will not be interpreted by hex as a hex number. One way to extract the hex substring:

Win8 Strawberry 5.8.9.5 (32)  Tue 06/07/2022 22:25:09
C:\@Work\Perl\monks
>perl

use strict;
use warnings;

my $str = '\x{aF}';

$str =~ m{ \A \\ x \{ ([[:xdigit:]]+) \} \z }xms;
my $hex_digits = $1;

print ">$hex_digits< \n";

my $hex_number_in_decimal = hex $hex_digits;
print "$hex_number_in_decimal \n";

^Z
>aF<
175
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Update: Another approach:

Win8 Strawberry 5.8.9.5 (32)  Sat 06/11/2022 15:18:47
C:\@Work\Perl\monks
>perl

use strict;
use warnings;

my $str = '\x{aF}';

my ($hex_digits) = $str =~ m{ [[:xdigit:]]+ }xmsg;
my $hex_number_in_decimal = hex $hex_digits;

print "'$hex_digits' == $hex_number_in_decimal decimal \n";

^Z
'aF' == 175 decimal
[download]

This approach can be useful when a string or record has been "validated" as to its structure and you know that certain substrings or fields are unambiguously present: these substrings/fields can then be easily and quickly extracted. Note the /g modifier on the m// match.