No quiero que la sopa quede tan salada como ayer.

Because after querer que when the subject changes, Spanish normally uses the subjunctive.

• Yo quiero... = I want...
• ...que la sopa quede... = ...that the soup turn out / end up

So:

• No quiero que la sopa quede... = I don’t want the soup to turn out...

Quede is the present subjunctive form of quedar.

This is very common in Spanish:

• Quiero que vengas. = I want you to come.
• No quiero que sea tarde. = I don’t want it to be late.

If you said queda, that would be the indicative, which does not fit after quiero que here.

Yes, quedar often means to stay, to remain, or to be left, but it also has another very common meaning: to turn out, to end up, or to come out (in a certain way).

In cooking and similar contexts, quedar is often used to describe the final result:

• La sopa quedó muy rica. = The soup turned out very tasty.
• El café quedó frío. = The coffee ended up cold.
• La tortilla quedó seca. = The omelette came out dry.

So No quiero que la sopa quede tan salada como ayer means: I don’t want the soup to turn out as salty as yesterday’s / as it was yesterday.

Because salada agrees with la sopa, which is a feminine singular noun.

• la sopa → feminine singular
• adjective must match → salada

Compare:

• la sopa salada
• el caldo salado
• las sopas saladas

This agreement is very important in Spanish adjectives.

Tan ... como means as ... as when making comparisons of adjectives or adverbs.

So:

• tan salada como ayer = as salty as yesterday

Other examples:

• tan alto como su hermano = as tall as his brother
• tan rápido como antes = as fast as before

Here the structure is:

• tan
  • adjective + como

So:

• tan
  • salada
    • como ayer

In natural English, it means as it was yesterday or as yesterday’s soup was.

Spanish often leaves out words that are understood from context. So como ayer is a shortened way of saying something like:

• como quedó ayer
• como la sopa de ayer
• como estaba ayer

The full idea is understood without repeating everything.

So although the literal wording is shorter, the meaning is: I don’t want the soup to turn out as salty as it did yesterday.

Because in Spanish, no usually goes directly before the verb it negates.

• Quiero... = I want...
• No quiero... = I don’t want...

This is the normal pattern:

• No sé. = I don’t know.
• No tengo tiempo. = I don’t have time.
• No quiero que venga. = I don’t want him/her to come.

The que introduces the subordinate clause after quiero.

In English, we can say:

• I want the soup to...

But in Spanish, when the subject changes, Spanish usually uses:

• Quiero que + [new subject] + subjunctive

So here:

• Yo = implied subject of quiero
• la sopa = subject of quede

That change of subject triggers the pattern:

• No quiero que la sopa quede...

You can think of que here as that, even though English often omits it.

Not with exactly the same meaning.

• No quiero que la sopa quede tan salada como ayer focuses on the result of the cooking process: you don’t want it to turn out that salty.
• No quiero la sopa tan salada... sounds more like I don’t want the soup that salty, which is possible in some contexts, but it does not express the idea of the soup ending up that way as clearly.

With cooking, quedar is especially natural because it refers to how the dish comes out in the end.

It could sometimes be omitted if the context is completely clear, but keeping la sopa makes the sentence more natural and clear.

• No quiero que quede tan salada como ayer. = possible if everyone already knows you are talking about the soup

• No quiero que la sopa quede tan salada como ayer. = clearer and more complete

Spanish often omits subject pronouns like yo, tú, él, but noun subjects like la sopa are kept when needed for clarity.

Quede is the present subjunctive, third person singular, from quedar.

The conjugation is:

• yo quede
• tú quedes
• él/ella/usted quede
• nosotros quedemos
• vosotros quedéis
• ellos/ellas/ustedes queden

It is present subjunctive in form, but in a sentence like this it often refers to a future result:

• No quiero que la sopa quede tan salada... = I don’t want the soup to end up so salty

That is normal in Spanish after verbs of wanting, emotion, influence, etc.

Not as naturally here.

• ser would be wrong, because ser salada would describe an inherent characteristic, not the result of cooking.
• estar would focus more on a state, but quedar is better for how something turns out.

Compare:

• La sopa está salada. = The soup is salty.
• La sopa quedó salada. = The soup turned out salty.

In your sentence, the speaker is talking about the result they want to avoid, so quede is the best choice.

Because ayer is an adverb meaning yesterday, and adverbs do not take articles in this kind of expression.

• hoy = today
• ayer = yesterday
• mañana = tomorrow

So:

• como ayer = like yesterday / as it was yesterday

You would not say como el ayer here.

The sentence is standard Spanish and works everywhere, but the use of quedar to mean turn out or come out is especially common and very natural in Spain, particularly in everyday speech and in cooking contexts.

For example, in Spain you often hear:

• La comida ha quedado muy bien.
• Te ha quedado riquísima la tortilla.

These mean things like:

• The food turned out really well.
• Your omelette turned out delicious.

So this sentence sounds very natural in Spain Spanish.