like / ilike with encode(bytea) not work with unicode

I have a system where I need to compare bytea values ​​(case insensitive in this case). For this purpose, I use encode to convert the bytea values ​​into strings which I then compare. This works as long as there is no unicode character in the array.

select 
    encode(cid, 'hex'),     
    cid = '\x3030386132323035'::bytea a,
    encode(cid, 'escape') = encode('\x3030386132323035'::bytea, 'escape') b,
    encode(cid, 'escape') like encode('\x3030386132323035'::bytea, 'escape') c,
    encode(cid, 'escape') ilike encode('\x3030386132323035'::bytea, 'escape') d
from history

When there are unicode characters in bytea, however, like/ilike do not work

select 
    encode(cid, 'hex'),     
    cid = '\x303030d0a2d095d0a1d0a231'::bytea a,
    encode(cid, 'escape') = encode('\x303030d0a2d095d0a1d0a231'::bytea, 'escape') b,
    encode(cid, 'escape') like encode('\x303030d0a2d095d0a1d0a231'::bytea, 'escape') c,
    encode(cid, 'escape') ilike encode('\x303030d0a2d095d0a1d0a231'::bytea, 'escape') d
from history

Can anyone explain what is causing this behavior?

That's because of the special meaning of backslashes in LIKE, ILIKE and SIMILAR TO syntax:

The default escape character is the backslash but a different one can be selected by using the ESCAPE clause. To match the escape character itself, write two escape characters.

Which doesn't play well with escape format:

escape
The escape format converts zero bytes and bytes with the high bit set into octal escape sequences (\nnn), and it doubles backslashes. Other byte values are represented literally.

On a simpler example:

select '\a' like '\a';--yields False

You can fix that by disabling or changing the default escape character: _{demo at db<>fiddle}

select    cid            as as_default
 , encode(cid, 'escape') as as_escape
 , cid = '\x303030d0a2d095d0a1d0a231'::bytea as a
 , encode(cid,'escape')
   = encode('\x303030d0a2d095d0a1d0a231'::bytea,'escape') 
   as b
 , encode(cid,'escape')
   like  encode('\x303030d0a2d095d0a1d0a231'::bytea,'escape') 
   as c
 , encode(cid,'escape')
   ilike encode('\x303030d0a2d095d0a1d0a231'::bytea,'escape') 
   as d
 , encode(cid,'escape')
   like  encode('\x303030d0a2d095d0a1d0a231'::bytea,'escape') 
   escape '' --escaping disabled
   as e
 , encode(cid,'escape')
   ilike encode('\x303030d0a2d095d0a1d0a231'::bytea,'escape') 
   escape '!' --escape character changed from default `\` to `!`
   as f
from history
where cid='\x303030d0a2d095d0a1d0a231'::bytea;

Simpler test:

select '\a' like '\a';           --False
select '\a' like '\a' escape ''; --True
select '\a' like '\a' escape '!';--True