BUG #17166: PREPARE without types inconsistent type resolving

The following bug has been logged on the website:

Bug reference: 17166
Logged by: Daniel Sonck
Email address: daniel(at)sonck(dot)nl
PostgreSQL version: 13.3
Operating system: Linux (Archlinux)
Description:

When executing the following statement, the type of $1 could not be
deduced:

SELECT * FROM my_table WHERE ($1 IS NULL OR col = $1);

However, when executing the following statement, the type of $1 could be
deduced:

SELECT * FROM my_table WHERE (col = $1 OR $1 IS NULL);

While both queries end result are the same, the first is more in line with
the meaning, saying that the optional parameter $1 may be NULL, or, if it's
not, results should be filtered by col = $1. It is rather curious that a
simple order affects the type of $1. I would imagine that, as $1 IS NULL has
no type implications, the col = $1 would determine the type of $1.