In der Wohnungsanzeige stand, dass die Einbauküche neu sei, aber bei der Besichtigung sah sie älter aus.

Wohnungsanzeige means apartment listing / apartment ad.

German very often builds nouns by combining smaller nouns into one word:

• Wohnung = apartment
• Anzeige = advertisement, listing

So Wohnungsanzeige is literally something like apartment advertisement. The -s- in the middle is a common linking sound in compound nouns.

Because in can take either the dative or accusative, depending on meaning.

Here it means in the ad / in the listing, so it describes a location, not movement. That requires the dative:

• in der Wohnungsanzeige = in the apartment listing

If there were movement into something, German would use the accusative instead.

Literally, yes, stand is the past tense of stehen = to stand.

But in German, stehen is also commonly used for written information:

• In der Anzeige stand ... = It said in the ad ...
• literally: It stood in the ad ...

So this is a very normal idiomatic use. English uses said; German often uses stand for text.

Because German main clauses follow the verb-second rule.

That means the finite verb must come in the second position. If some other element comes first, the subject usually comes after the verb.

So:

• In der Wohnungsanzeige = first position
• stand = second position
• then the rest follows

The basic pattern is:

• In der Wohnungsanzeige stand, ...

not

• In der Wohnungsanzeige die Einbauküche stand ...

Dass means that and introduces a subordinate clause.

The sentence is reporting what the ad stated:

• In der Wohnungsanzeige stand, dass ...
• The ad said that ...

German often uses dass exactly where English uses that in this kind of sentence.

There are two things happening here.

1. Subordinate clause word order
After dass, the finite verb goes to the end:

• dass die Einbauküche neu sei

That is normal German subordinate-clause word order.

2. The verb form is sei
That is not the normal present tense. It is Konjunktiv I, often used for reported speech. So the sentence is presenting the information as something the ad claimed.

Sei is Konjunktiv I of sein. German often uses it in indirect or reported speech.

So:

• Die Einbauküche ist neu. = The fitted kitchen is new.
• In der Anzeige stand, dass die Einbauküche neu sei. = The ad said that the fitted kitchen was new.

Using sei creates a bit of distance: this is what was claimed, not necessarily what the speaker confirms as true.

Why not war? Because the original claim being reported is basically it is new, and German often keeps that idea in reported speech with sei, even though the main verb stand is in the past.

Yes, that is possible, especially in less formal German.

• ... dass die Einbauküche neu ist is common in everyday speech
• ... dass die Einbauküche neu sei is more formal or more clearly marked as reported speech

So sei is grammatically very appropriate here, but ist would also be understandable and common in many contexts.

Einbauküche usually means a built-in kitchen or fitted kitchen.

It refers to a kitchen with installed cabinets and often built-in appliances, rather than just an empty room or a few movable kitchen items.

This matters a lot in German housing ads, because whether a flat includes a kitchen is often specifically mentioned.

Because neu here is a predicate adjective, not an adjective directly in front of a noun.

Compare:

• die neue Einbauküche = the new fitted kitchen
  Here the adjective comes before the noun, so it gets an ending.

• die Einbauküche ist neu = the fitted kitchen is new
  Here it comes after sein, so it does not get an ending.

In your sentence, it is the second type:

• die Einbauküche neu sei

So neu stays unchanged.

Bei means something like during, at, or on the occasion of here.

• bei der Besichtigung = during the viewing / at the inspection

The noun Besichtigung means a viewing or inspection, especially of an apartment or house.

Also, bei always takes the dative, which is why it is der Besichtigung.

Here Besichtigung means the visit where a prospective renter or buyer goes to see the apartment in person.

In housing contexts, it is often best translated as:

• viewing
• apartment viewing
• sometimes inspection

So bei der Besichtigung means when they went to see the apartment.

Because the verb is aussehen, meaning to look / to appear.

It is a separable verb:

• infinitive: aussehen
• past tense in a main clause: sah ... aus

So:

• sie sah älter aus = it looked older

This split is normal in main clauses with separable verbs.

Älter is the comparative form of alt:

• alt = old
• älter = older

Here it means the kitchen looked older than expected or older than something described as new should look.

So it does not necessarily mean the kitchen was extremely old. It means it seemed less new / more aged than the ad suggested.

Sie refers to die Einbauküche.

That noun is feminine:

• die Einbauküche

So the matching pronoun is:

• sie = she / it

In English we would say it looked older, but German uses sie because Einbauküche is grammatically feminine.

German often uses the Präteritum past tense for narration, especially in writing and in more neutral storytelling style.

So:

• stand
• sah

are very natural here.

In everyday spoken German, many speakers might prefer Perfekt for some verbs, but sein, modal verbs, and a few common verbs often still appear in Präteritum. In written or polished narrative German, stand and sah are completely normal.

Yes. That is exactly the point of aber.

The structure is:

• the ad claimed the kitchen was new
• but
• during the viewing, it looked older

So the sentence contrasts advertised description with actual appearance. That is why sei works especially well: it presents the first part as a reported claim rather than a confirmed fact.