This.
For restaurants that have good allergy control practices, stating that one has a food allergy to "x" will trigger a protocol that involves a fair bit of work on the part of the restaurant. At the least it should mean verification of ingredients, and that your food will be prepared separately on a freshly cleaned surface using clean utensils. For many it means that ONE person is responsible for cooking the mean from end to end [whereas normally multiple people may be responsible for different parts], and in some restaurants that person will be a supervisor or manager or senior chef. Some restaurants use a special "allergy kit" with color coded utensils etc -- all clean of course. Some kitchens have a special area of the kitchen that is used, while others will make a clean area [and not just a wiping down, a good process is more thorough]. Other steps may be involved as well. And of course, modifications to the actual recipes may be needed to exclude or substitute things.
For ingredients it means some things won't be done or will be done differently out of an abundance of caution. So for example, there is one restaurant we go to where I always get a steak. They cook some seafood on one end of the grill and the steaks on the other end, with space in between, but the chefs and managers have always said that even though there shouldnt be cross-contamination out of an abundance of caution they would prefer to pan fry the steak and confirm with me if that is ok, which of course it is. I am glad they have the conversation with me [and I have had some amazing food allergy conversations with restaurant staff over the years - some are so knowledgable and passionate]. It can sometimes mean a relatively bland meal as sauces and spices may need to be cut out and there may not be ready replacements.
All of those things are done to prevent both the allergen being present as an ingredient and to prevent it accidentally being introduced through cross-contact/contamination, where even trace amounts can trigger reactions.
This is different from dealing with a food preference, where while avoiding the ingredient is important, trace amounts from cross contact/contamination are not likely to be an issue nor have the potential to trigger a life-threatening reaction or illness. The kitchen process is usually different.
This is part of where the frustration of restaurants comes in when people claim to have a food allergy and then do things like "cheat" and have a bit of their family member's dessert that contains the supposed allergen, or say "well just a little is ok" when told something has to be excluded because it contains the ingredient. When things like that happen enough, you end up with the eye rolling, disbelief and other issues that people with genuine food allergies sometimes experience when they try to eat out. If you google, there have been many articles written on the topic.
As someone with anaphylaxis to multiple foods, when I eat out, my food is my food. There is no eating from someone else's plate as that food hasn't been prepared with the allergen in mind; though others at my table may steal from MY plate because they don't have allergies and want to e.g. try my wedge potatoes when they got the normal hash browns ;-)
Back to the OP's question.
I don' think there is a problem with saying you have a soy allergy, provided you understand the implications of doing so for the kitchen and your meal, and that you are consistent with it throughout [eg no stealing a fry from someone else's plate.. they may be pre-cooked in some soy oil...].
If you aren't comfortable with that, then explain that your doctor has you on a soy-free diet or that you can't have soy for medical reasons. You may be asked if trace amounts or cross-contamination are ok, so decide ahead of time what your answer would be. [if you decide trace amounts are not ok, you can be upfront: you can't have soy for medical reasons and avoid even trace amounts].
Also, as another poster pointed out, certain forms of soy are not considered allergens under food labelling laws, so if you also need to avoid those, you need to include that when having the conversation with the staff. Be clear and specific.
Finally, regardless of which choice you make, I strongly suggest you consider carrying a chef card. With just one "allergen" you can make them business card size if you want [mine with more are 4x6 cards]. Carry them with you wherever you go that way you always have some on hand. I have found Chef cards both help tremendously with communicating my allergies, as well as demonstrate that I am serious about them.
Some resources you may find useful:
FARE's dining out resources:
https://www.foodallergy.org/resources/dining-out
FARE's food allergy chef cards (templates in multiple languages):
https://www.foodallergy.org/resources/food-allergy-chef-cards
Allergy & Anaphylaxis Australia's chef card templates:
https://allergyfacts.org.au/resources/chef-card-template
Finally, a couple articles about the issue of people claiming a food allergy when they don't have one:
https://www.cbc.ca/news/business/food-allergies-resaurants-1.4127854
https://www.allergicliving.com/2017/02/16/consequences-faking-food-allergy/
Good luck !
SW