What's up with Gluten Free in Austria?

I can imagine your frustration. Sounds like either a CYA situation or because of close proximity in the kitchen, there may be traces either by nearness to gluten, or someone inadvertently using a contaminated spoon or utensil.
Are you familiar with happycow dot net website? Has been around for years and lists shops and restaurants for allergic and vegan/vegetarian folks. You may want to check there to add to your options.

I see lots of gluten free (glutenfrei) options in Vienna. It is not unusual.

Have a look at these links:

https://www.happyceliac.com/de/glutenfrei-in-wien/

https://www.glutenreise.at/glutenfrei-in-wien-restaurants/

https://www.herold.at/blog/glutenfrei-essen-wien-glutenfreie-restaurants-wien/

These articles are in German, but you’ll get the idea.

I did not notice those “A” designations when we were in Vienna, so I looked at the menu for Cafe Schwarzenberg, where we had lunch several times. I see what you mean; most dishes (but not all, and not coffee) have the A designation.

https://www.cafe-schwarzenberg.at/fileadmin/Bibliothek/Speisekarte/Speisekarte.pdf

But in many cases, as with Beef Tatar and the Smoked Salmon, the A is because the plate is served with a piece of toast. Or the clear beef broth, with a dumpling.

Most of the main dishes will have breading or a sauce, so lots of gluten there. But they have two salads, one with grilled turkey breast and one with grilled prawns, without the A designation. Also one kind of Wurst (but not the other kind). And omelettes.

I suspect the places that put an A beside everything, including coffee, are just being lazy. Or CYA as suggested above. As I understand it, the EU regulations on labeling are very strict. For example, as our guide on a hiking trip in France explained, bread labeled “gluten-free” must be baked in a dedicated, separate facility, not simply made with GF ingredients. As a result, they were unable to provide gluten-free bread for my lunch sandwiches on some of our stops in small villages. Instead, I got a nice tomato, mozzarella, and basil salad.

I highly suspect it's a CYA move. My son is gluten- and dairy-free, and he eats lots of things that aren't "certified" either way because they use shared equipment (e.g Clif bars are both, but are not labeled gluten-free because of shared equipment with wheaty things). I'm sure you're used to what is and is not GF, so I would just do your best. We know that usually roast chicken and potatoes are GF even if there's the mystery "A" next to them. Probably worth it to bring a couple of boxes of granola bars, etc. that he can eat with you.

Thanks for the input. CYA makes sense - or simply things served with bread on the side. Perhaps the coffee comes with a biscuit, who knows. I'm hoping in some cases we can just request the side be left off if it's an issue of a gluten-free dish and a separate side, not mixed together. We've been to about 5-6 countries since he was diagnosed celiac and Austria seems the most challenging so far. However it looks doable so I'm not too worried. Italy and Mexico were easiest (Italy because there's amazing awareness and most restaurants had GF pasta on-hand, Mexico because of corn based everything).

Emily, thanks for the restaurants. I hadn't seen some of those, they are going on my map! Maria, I have used that website in the past but forgot about it, thanks for the reminder!

For consideration, Spain would be a comfortable country to visit. Not necessarily with replacement baking, but well marked menus.
I need to avoid or reduce gluten but not to the extent of a celiac. You state your son is celiac which would mean any traces or cross contamination would make him sick. For his sake and to reduce confusion, please be consistent with your labeling and the allergy cards you take. Medically, they are not really interchangable, though your OP sort of implies some leniency in exposure is acceptable. Keeping a celiac kitchen is not an easy matter.
You may also do some searches for blogs on celiac eating in the relevant towns. I find them reassuring.

I guess the positive is that they are indicating if a food has gluten, or might possibly have come into contact with gluten. It is a bit like statements in the US where they do not guarantee that items have not come into contact with nuts or dairy, even though the item may not contain them.

For examples you have seen:
Roast Chicken: often dredged in flour to help the skin brown. Potatoes: flour may be used to thicken or "set" the dish, especially with something like Gnocchi, dumplings, or a casserole type dish, especially if cheese is involved. Salad: often served with croutons, potentially even some dressings have gluten in them (thickeners) Coffee: the bean itself, no; but it is not unknown to roast coffee with other grains to "mellow" them, or just stretch them; beyond that, creamers, whipped toppings, and other additions might contain gluten.

Generally, I have found Germany, and I have heard it is similar in Austria, to be the most transparent about Gluten, better than the US. I do suggest, as above, having some type of card that explains your dietary needs.

I had been online looking at neighborhoods around my hotel in Vienna and noticed there was a McDonald's. Since I love a good Diet Coke fountain pop, I decided to take a quick look at their menu to see what the pop options are over there. I noticed when doing this that they have a whole gluten free section of their menu. If all else fails, that's always an option to have in your back pocket.