Утро тоже было напряжённым, но, когда мы наконец всё обсудили, я облегчённо вздохнул.

Because it is part of the predicate after было (was).

In Russian, when a noun or adjective describes what something was / became / will be, the predicate is very often put in the instrumental case:

• Утро было напряжённым. = The morning was tense.
• Он стал врачом. = He became a doctor.

Here:

• утро = neuter singular subject
• напряжённым = instrumental singular, agreeing with утро

This is a very common pattern after быть, стать, оказаться, and similar verbs.

Yes, you may hear that too, especially in more conversational speech. But было напряжённым is very standard and natural.

A rough way to think about it:

• напряжённым (instrumental) is the classic predicate form after было
• напряжённое (nominative) is also possible in some contexts, often sounding a bit more colloquial or direct

For learners, было + instrumental is the safest pattern to remember.

Тоже means also / too.

Here it applies to the whole idea of the morning being tense:

• Утро тоже было напряжённым
  = The morning was tense too / as well.

So the speaker is implying that something else was tense before this, and now the morning is being added to that list.

Position matters a little in Russian, but тоже often comes after the word it is attached to or near the part being emphasized.

Because it refers to a completed action: the discussion reached its end.

• обсудили is perfective past plural from обсудить
• It means discussed completely / finished discussing

The sentence means that the sigh happened after the discussion was fully finished.

Compare:

• когда мы всё обсуждали = while we were discussing everything / when we used to discuss everything
• когда мы всё обсудили = when we had discussed everything / when we finished discussing everything

The perfective verb is used because the completion is important here.

Because всё means everything, while все usually means everyone or all.

• всё обсудили = discussed everything
• все пришли = everyone arrived

So in this sentence, всё is the direct object of обсудили.

A useful contrast:

• Мы всё обсудили. = We discussed everything.
• Мы все обсудили это. = We all discussed it.

In the second sentence, все refers to we all, not everything.

Because Russian word order is flexible, and всё обсудили is a very natural order.

The neutral version here is:

• мы наконец всё обсудили

This often sounds smoother than:

• мы наконец обсудили всё

Both are possible, but they can sound slightly different in emphasis:

• всё обсудили highlights the idea of everything
• обсудили всё can sound a bit more like the speaker is stressing that literally nothing was left undiscussed

In many everyday sentences, Russian places short objects like всё, это, его before the verb.

Here наконец means finally / at last.

It suggests that the discussion took a while, or that reaching the end was important or difficult:

• когда мы наконец всё обсудили
  = when we finally discussed everything / when we had finally talked everything through

It often carries a feeling of relief, impatience, or completion.

Because когда мы наконец всё обсудили is a subordinate clause inserted into the main sentence.

Structure:

• Утро тоже было напряжённым,
• но,
• когда мы наконец всё обсудили,
• я облегчённо вздохнул.

The main clause is:

• я облегчённо вздохнул

The когда clause tells when that happened, so it is set off by commas.

The comma after но appears because но is followed by a full subordinate clause, not directly by the main clause.

Облегчённо means with relief / relievedly.

It is an adverb, because it describes how the speaker sighed:

• вздохнул как? — облегчённо
  = sighed how? — with relief

Russian often uses adverbs where English might prefer a phrase:

• я облегчённо вздохнул
  = I sighed with relief

A close alternative in Russian would be:

• я вздохнул с облегчением

Both are natural.

Because Russian past tense agrees with the gender of the subject.

With я in the past tense:

• я вздохнул = I sighed (male speaker)
• я вздохнула = I sighed (female speaker)

So this sentence tells us that the speaker is male, unless it is just being used in a grammar example.

Because it agrees with утро, which is a neuter singular noun.

• утро = neuter singular
• therefore было = neuter singular past tense of быть

Compare:

• день был напряжённым = The day was tense
• утро было напряжённым = The morning was tense
• неделя была напряжённой = The week was tense

The form of the past-tense verb changes with gender and number.

Yes: it sets the scene and topic immediately.

Russian often puts the topic first:

• Утро тоже было напряжённым...

This sounds like: As for the morning, that was tense too...

The sentence then moves from background information (the morning was tense too) to the main event (I sighed with relief once we had discussed everything).

That topic-to-comment flow is very natural in Russian narration.

It has two main parts joined by но:

1. Утро тоже было напряжённым
   = background situation

2. я облегчённо вздохнул
   = main result/action

Inside the second part, there is a time clause:

• когда мы наконец всё обсудили

So the logic is:

• The morning was tense too,
• but when we finally discussed everything,
• I sighed with relief.

This kind of layered structure is very common in Russian narrative style.