In the PGADMIN4 server version, you have programmed the COPY command. For a simple user (without right on the server), the \ COPY meta command will be more useful.
pgAdmin should (I've only used it minimally and not v4) indeed implement file export/import via SQL "COPY" (and a custom UI, not a query window) - and would arrange for the proper command syntax and making the relevant data available on the server's stdin (COPY FROM) or take the server's response via stdout (COPY TO) and turn it into a file for you.
If you simply type "COPY" into a SQL query window and send it to the server pgAdmin probably doesn't do anything special and you end up with whatever normal behavior such a copy would entail. That probably includes placing non-SQL text (i.e., csv data) into the query screen and sending it to the server for processing - just like you can in a psql script (i.e., COPY in psql works with inline data).
pgAdmin doesn't have a text/CLI language that would control the application like psql does. Adding it simply for "\copy" is likely to fail a cost/benefit analysis.
In short, you can (probably) do everything you need to with the tools as they exist today. You might need to learn more about how they work, though.