Hot standby writable?

Hello,

I have a cluster with a streaming replication primary, and two hot standbys
(PostgreSQL 12.8). Today I connected to one of the standbys, and
accidentally executed a CREATE TABLE statement. To my surprise, it created
the table, and the change was visible on the primary and also on both
standbys. I examined this behaviour, and found the following. If I connect
to the standby using psql cli then the database is read-only, as expected:

test=> create table test(id int8 not null primary key);
ERROR: cannot execute CREATE TABLE in a read-only transaction

But if I connect to the standby using dbeaver, then somehow the database
becomes writable. Dbeaver runs on my computer, the standby runs on a
separate network and the connection is established through an ssh tunnel.
The primary instance is located inside another network (actually in a
different datacenter), and it is behind a VPN. In other words, it is
technically impossible for dbeaver to connect to the primary. And yet
somehow it can make changes in the database.

Am I missing something? Is there a possibility that the hot standby
forwards SQL statements to the primary? I was not aware of such
functionality.

Right now, it imposes a security risk in our environment, so I would really
like to know how this works.

Thanks,

Laszlo