REGEXP / REGEXP_REPLACE operations with empty source string match, but do not replace

REGEXP_REPLACE does not replace a match with source string empty string (''), but REGEXP does match the empty string with a similar regex (.*). This seems inconsistent.

Examples:

Example 1. REGEP_REPLACE with empty source string: does not replace

SELECT REGEXP_REPLACE('', '^(.*)$', '\\1 hello');

result: ''

Example 2. REGEXP with empty source string: does match

select '' REGEXP '^.*$';

result: 1

Example 3: compare with perl:

echo '' | perl -p -e "s/.*/hello/"

Result: hello

I posted the question on Stack Overflow and was referred here.

I wasn't sure if this was really a bug, but it seems inconsistent - MariaDB uses https://mariadb.com/kb/en/pcre/, the perl command line as well as regex101 using perl do a replacement on the empty string.