There are eight major versions/editions of The Joy of Cooking. [For more detail see here.]
My copy, inherited from my mother, is the 4th edition, 1951; it's a 1953 reprinting that includes the best index up to that point -- a good thing, as the book had grown to more than a thousand pages by that time.
I'm sure you'll want to get a first-hand look at the different editions, because there's much more to the treatment of garlic in each of them than whether and how it appears in the two recipes you've chosen.
None of the recipes for chicken soup or chicken broth in the 4th edition include garlic.
On the other hand, there's this, as part of a discussion of 'Additions that Lend Distinction to Food', p. 78 in the introduction to the extensive Luncheon and Supper Dishes section:
:: Charles Rector has called garlic the vanilla of vegetables. Use it to rub the inside of a salad bowl or a skillet. If you like a lot of it and don't mind the consequences, mince it and add it to food, preferably to hot butter, or add a whole skinned clove of garlic and fish it out before the food is served. Of course the humble --- well, not so very humble -- onion is a good understory; so is the leek. ::
Garlic is used in the following ways in relation to spaghetti sauce:
In 'Italian spaghetti', chopped garlic is sauteed with onions, carrots, and celery before the ground meat is added, followed by tomatoes and simmering. The thickened sauce is layered with cooked spaghetti in a dish before serving. In 'Meat sauce for spaghetti', sliced garlic is heated in olive oil and removed as it begins to brown; the garlic-infused oil is used to saute chopped onions before the meat and tomatoes etc. are added for a long simmer. The sauce is combined with cooked spaghetti to coat it before serving.
Garlic is used in many other ways [recipes in brackets]:
- mashed with a little salt and spread on bread, followed by melted butter, then baked. [Garlic bread]
- halved cloves steeped in hot vinegar, allowed to cool and stored for two weeks before being strained out. [Garlic vinegar]
- whole peeled clove as one of the flavorings (with bay, celery, and cayenne) in water used to boil shrimp. [Boiled shrimp]
- well-crushed cloves with minced shallots, parsley, and celery in softened butter, stuffed in shells with the snails [Snails]
- sliced cloves as one of the flavorings in wine used to cook mussels, with chopped celery, parsley, and butter [Moules mariniere]
- whole peeled cloves steeped with olives in oil for 24 hours [Garlic olives]
- chopped garlic as one of the flavorings in a curry sauce, with coconut, milk, sauteed chopped onion, chopped fresh ginger, curry powder, et al. [Indonesian rice table]
- minced garlic, among a mix of finely chopped vegetables (celery, green peppper, parsley) stuffed into slits in fish before baking [Baked red snapper with vegetables]
- sliced garlic steeped in olive oil for 24 hours to produce garlic oil, used to flavor croutons [Caesar salad]
- cut clove rubbed on both sides of a dry or toasted piece of bread, which is placed in the bowl with salad ingredients, left there while the salad is tossed with the dressing, and removed before serving, "giving to salad a delicate touch of this pungent product" [introductory passage in Salads section]
This list gives some idea why limiting yourself to spaghetti sauce and chicken soup is not very informative, and I hope inspires you to put your hands on other early editions.