Learn Hardcore German: Die Chefin erklärt, diese Woche sei nur eine Übergangsphase im Projekt. - The boss female explains this week is only a transitional phase in the project.

Direct speech:
Die Chefin erklärt: "Diese Woche ist nur eine Übergangsphase im Projekt."
Indirect speech:
Die Chefin erklärt, diese Woche sei nur eine Übergangsphase im Projekt.

Using sei shows that this is what the boss says or claims, not necessarily what the speaker confirms as true. It’s a stylistic and sometimes semantic marker of “reporting someone else’s words”.

Could we also say „... dass diese Woche nur eine Übergangsphase im Projekt ist“?

Yes. A very common alternative is:

Die Chefin erklärt, dass diese Woche nur eine Übergangsphase im Projekt ist.

Differences:

With „dass“ + ist:
→ More colloquial, neutral, very common in spoken German.
→ Grammatically an ordinary subordinate clause (Verb at the end).
Without „dass“ + sei:
→ More typical of written language, news reports, more formal style.
→ Uses Konjunktiv I to mark reported speech.

Both are correct. In everyday conversation, „..., dass ... ist“ is more likely.

Is sei Konjunktiv I or Konjunktiv II, and how is it formed?

Sei is Konjunktiv I, 3rd person singular of sein.

The relevant forms of sein:

Indicative present: ich bin, du bist, er/sie/es ist, wir sind, ihr seid, sie sind
Konjunktiv I: ich sei, du seiest, er/sie/es sei, wir seien, ihr seiet, sie seien
Konjunktiv II: ich wäre, du wär(e)st, er/sie/es wäre, wir wären, ihr wär(e)t, sie wären

So in this sentence, sei clearly belongs to Konjunktiv I, used for indirect speech.

Could we also say „diese Woche wäre nur eine Übergangsphase“ instead of „sei“?

You could, but it would be unusual and slightly change the feel:

sei = standard Konjunktiv I for reported speech, neutral.
wäre = Konjunktiv II, which often suggests doubt, unreality, or distance.

Die Chefin erklärt, diese Woche wäre nur eine Übergangsphase ...
can sound as if the speaker is more skeptical about the statement, or as if this is hypothetical. In normal neutral reported speech, sei is preferred.

Why is the verb in the reported clause in second position (sei) and not at the end, like in other subordinate clauses?

There are two different structures:

With dass:
- Die Chefin erklärt, dass diese Woche nur eine Übergangsphase im Projekt ist.
  → Subordinate clause with dass → verb goes to the end.
Without dass, using Konjunktiv I:
- Die Chefin erklärt, diese Woche sei nur eine Übergangsphase im Projekt.
  → This is indirect speech without a conjunction.
  → The clause keeps verb-second (V2) word order, like a main clause.

So:

dass-clause = verb-final
indirect speech without dass = verb-second with Konjunktiv I

What is the nuance of erklärt compared to sagt or meint?

sagt = says (neutral, just reporting speech)
meint = thinks / is of the opinion (emphasizes opinion/attitude)
erklärt = explains / declares (suggests some kind of justification or clarification)

Die Chefin erklärt... implies that she is clarifying something to others, not just casually mentioning it. It can also sound slightly more formal than sagt.

What does Übergangsphase mean exactly, and how is the word formed?

Übergangsphase is a compound noun:

der Übergang = transition, passing from one state to another
die Phase = phase, stage

So die Übergangsphase = a transitional phase, an intermediate stage.

In this sentence, it means that this week is just a temporary stage in the project, not the final or normal state.

Why is it „im Projekt“ and not something like „in dem Projekt“ written out?

Im is simply the contraction of in dem:

in dem Projekt → im Projekt

Both are grammatically correct. The contracted form im is far more common in normal usage. There’s no special nuance here; it’s just the usual contraction.

Why is it „die Chefin“ and not „der Chef“?

German marks grammatical gender:

der Chef = male boss
die Chefin = female boss

So die Chefin indicates that the person is female.
Both Chef and Chefin are nouns, so they are always capitalized.

Is the tense of erklärt here present or past? How would I say “The boss explained that this week was only a transitional phase”?

In the given sentence, erklärt is present tense:

Die Chefin erklärt, ... = The boss explains / is explaining...

For a past context:

Die Chefin erklärte, diese Woche sei nur eine Übergangsphase im Projekt.
→ Past reporting verb + Konjunktiv I.
German often keeps Konjunktiv I in the present form even when the reporting verb is past. The time reference is clear from context.

If you don’t want Konjunktiv:

Die Chefin erklärte, dass diese Woche nur eine Übergangsphase im Projekt war.

This is also fine, especially in spoken German.

Could I move nur or diese Woche to other positions, and would that change the meaning?

Yes, word order can shift the emphasis slightly:

Diese Woche sei nur eine Übergangsphase im Projekt.
→ Neutral focus; “this week” as the topic.
Nur diese Woche sei eine Übergangsphase im Projekt.
→ Focus on nur diese Woche = only this week (and not other weeks).
Diese Woche sei eine Übergangsphase nur im Projekt.
→ Very unusual; would sound strange. Not recommended.

In your original, nur before eine Übergangsphase restricts the type of thing this week is:
“This week is only a transitional phase”, not something more dramatic.

Is this sentence more formal or informal, and where would I expect to see this style?

The structure with Konjunktiv I and no „dass“ is:

More formal / written style.
Common in newspapers, official reports, formal minutes, etc.

In casual spoken German, people would much more often say:

Die Chefin sagt, dass diese Woche nur eine Übergangsphase im Projekt ist.

So your original sentence sounds like something you might read in a report or written summary of what the boss said.