Is IDENTITY continuous in new versions of PostgreSQL?
The term is IDENTITY, not IDENTIFY. (I fixed it in your question.)
IDENTITY columns (GENERATED { ALWAYS | BY DEFAULT } AS IDENTITY) are based on a SEQUENCE just like the older serial columns. You have to expect gaps in the serial numbers with either, that's in the their nature, and nothing to worry about.
Differences are addressed in my answer on stackexchange (where you obviously found the code to convert your serial to an IDENTITY column):

How to change a table ID from serial to identity?

But nowhere did I suggest that the conversion would remove gaps in the ID space. Or that this would be desirable. If you positively think you need that, consider:

Compacting a sequence in PostgreSQL

It starts with a similar disclaimer like you already received in the comments (and some alternatives):

First off, gaps in a sequence are to be expected. Ask yourself if you really need to remove them. [...]