Does it matter to convert integer primary key into equivalent string? In a PostgreSQL DB, I have a sortable bigint primary key, which is a bit verbose in terms of readability.
I want to encode it as base36 or base64, like using char(n). In theory the number of bytes should be the same as before, so it does not take more space. Is that correct?
Are there other concerns? For example sorting, collation?
There are potential performance differences and sorting differences (collation dependent) per this DBA.StackExchange answer and it's linked answers such as this one. I highly recommend reading through all the information referenced in that answer.
These sections of the above linked articles are specifically relevant:

There is no performance difference among these three types [char,
varchar, text]...


Short answer: integer is faster than varchar or text in every aspect.

Therefore integer (and BIGINT) is more performant of a data type, even of equal data length.