RS='.^' apparently ignores the RS setting

[Ed Morton]

We were just having a conversation on comp.unix.shell about various RS 
settings and someone pointed out that you should be able to use 
`RS='$^'` to read a file because a start-of-string anchor can never 
appear after an end-of-string anchor (I mentioned `RS='^$'` as IMHO a 
better existing alternative).

At first I thought `$^` just meant that pair of literal characters but 
apparently the meaning of `$^` differs between BREs and EREs because:

    $ echo 'a$^b' | grep '$^'
    a$^b

    $ echo 'a$^b' | grep -E '$^'
    $

    $ echo 'a$^b' | sed 's/$^/X/'
    aXb

    $ echo 'a$^b' | sed -E 's/$^/X/'
    a$^b

So I read 
https://pubs.opengroup.org/onlinepubs/9699919799/basedefs/V1_chap09.html#tag_09_04_09 
which I thought was saying you could use any character before the `^` 
and it wouldn't match which was supported by this test:

    $ printf 'ax^b\nax^b\n' | awk 'BEGIN{RS="x^"}{print NR, $0}'
    1 ax^b
    ax^b

but then I can't explain this where gawk is apparently completely 
ignoring the RS setting:

    $ printf 'a.^b\na.^b\n' | awk 'BEGIN{RS=".^"}{print NR, $0}'
    1 a.^b
    2 a.^b

Is that a bug?

$ gawk --version
GNU Awk 5.1.0, API: 3.0 (GNU MPFR 4.1.0, GNU MP 6.2.1)

Regards,

    Ed.