October in Trieste - stylish solution for rain&wind

If you don’t own a really excellent raincoat, that is what I would invest in. Something that has an inner liner that you can remove would be great. I had one from Boden for years till I wore it out, but not sure if they currently sell a similar model. I have one that is north face with a removable light puffer, but I think you want something less sporty, more like a trench or a Macintosh. I don’t think you’ll need a puffer in early October.

I have a light raincoat from Athleta that I find attractive, you might check there to see if they have a medium weight one.

I take a trenchcoat on every trip to Europe and feel that it's versatile. Past versions have had a zipout liner, which is a good option. My current version is a tightly woven cotton, no zipout lining, and it has served me well even when the temps are in the high 30s (F). It's water resistant, not waterproof, but if it was pouring buckets I would be seeking shelter indoors anyway. It's worked just fine even in heavy rain (while also having an umbrella). My version does not have a hood, which I personally don't like anyway, so I have a matching bucket hat that I keep in my pocket if it looks like rain.

I will say, wherever I've been in Europe, even in big cities like Milan or Paris, I'm not seeing many trenchcoats. I see many, many more casual jackets (but keep in mind, many of those people are locals who may have a nicer coat at home).

While I'm a trenchcoat fan, given your planned itinerary, a rain jacket and a puffer coat would work well too. My spouse and I giggle at the temperature (that seem plenty warm to us) that we see Italians in particular wearing their puffer coats. If you want to blend in with the locals, probably the raincoat and/or puffer coat would do that..

Technical gear is having a fashion moment so you can wear outdoor clothing in the city now and look perfectly stylish - half of East London are wearing Salomon shoes to go for no more than a coffee. You will never find ‘fashion’ clothing that functions as well as proper outdoor clothing and once you go down that route you’re never looking back.

If price isn't a factor you might look at Protected Species, based in the UK, for their style and function. I have the City Walker style from several years ago. It is fully wind and rainproof with an excellent hood. I wore it in torrential rain in Scotland hiking as well in various cities. It's roomy enough for a sweater under, if the weather is cold.
It's beautifully crafted and washes well.
I bought their fleece- lined jacket, too, for the PNW but it runs large and doesn't "read" stylish, more like a regular parka.

Husband and I both have 3 in 1 jackets from Columbia. While I am not completely enamored of having “Columbia” stitched across the jacket, for us the pros of the jacket for outweigh the cons. It is water proof with a zip out lining. We put the zip out lining in a compression cube and have an extra pillow for our lower backs during the flight. Keeping the lining out we have a rain jacket or a light weight coat, and with the lining in, we have a very warm coat. They are not dressy but they are very utilitarian and work well for us.
We compared prices between Amazon and direct from Columbia and at the time (last year) purchased directly from Columbia. Be sure and read the reviews, I had to purchase mine in a smaller size; even accounting for possible layers and the lining in the winter, I had to size down.

Athleta has attractive and packable raincoats. I bought one with a little extra room so I can wear a vest or sweater with it. The perfect solution for changeable October weather.