Gurgling in the drainage

Hello, I am new here and don't know if this is the right forum for my question, if not, please let me know!

We moved into an old (1960) house and will soon get a new kitchen.
Now, the thing is, with the old kitchen, whenever water runs from the sink, the drain makes a terrible gurgling noise.
I think the sink is not vented.
The previous owner said it was always like that and it didn't bother him.
Well, it bothers me a lot and I am considering what can be done.

The easiest thing would be if you could install some kind of vent in the sink drain behind the trap in the drain fitting, I thought...
Is there something like that and what can I do about unpleasant odors?
How can I tell if there really is no vent without breaking open the walls? You can't see a pipe on the roof nearby... but also nowhere else in the attic, and otherwise we have no gurgling problems. How was ventilation built in the past???

Who can help me?

Best regards, Suxxi

Look in the attic to see if there might be a pipe ending under the roof.

We have no attic, the rooms go right up to the roof. (Holzschalung, Dämmung *:confused:*, Teerpappe, Ziegel) If anything - then the pipe can only end directly under the tiles.... and there are still a few inaccessible corners behind the knee walls.... But you can't get there without a hammer. :(