Новая грамматическая тема: конструкция «не то чтобы ..., но ...» помогает говорить мягче и точнее.

It is a softening pattern. A natural English equivalent is:

• not exactly ..., but ...
• it’s not that ..., but ...
• I wouldn’t quite say ..., but ...

It lets you avoid sounding too blunt.

Example: Не то чтобы он ленивый, но работает медленно.
= It’s not exactly that he’s lazy, but he works slowly.

Not really. In this expression, не то чтобы works as a fixed chunk.

So it is better to learn не то чтобы as one unit, rather than trying to translate чтобы literally.

In other words, this is an idiomatic construction, not a normal purpose clause.

Не ..., а ... is more direct and categorical:

• Он не грубый, а прямой.
  = He isn’t rude, he’s straightforward.

Не то чтобы ..., но ... is softer and more nuanced:

• Не то чтобы он грубый, но иногда звучит резко.
  = It’s not exactly that he’s rude, but sometimes he sounds harsh.

So the construction in your sentence is used when you want to sound more careful, polite, or precise.

Because тема is a feminine singular noun in the nominative case.

The adjectives must agree with it:

• новая — feminine singular nominative
• грамматическая — feminine singular nominative
• тема — feminine singular nominative

So the whole phrase means a new grammar topic.

The colon introduces what the new topic is.

So the structure is:

• Новая грамматическая тема:
  New grammar topic:
• then the sentence tells you what that topic is.

This works very similarly to English.

Because конструкция is the subject of the sentence, and it is singular.

So the verb is also singular:

• конструкция помогает
  = the construction helps

If the subject were plural, the verb would change:

• конструкции помогают
  = the constructions help

Because помогать can be followed by an infinitive to mean help to do something.

So:

• помогает говорить
  = helps [someone] speak

Russian often leaves the person general or understood from context. Here it means something like:

• helps you speak
• helps people speak

If you want to name the person, Russian often uses the dative:

• Конструкция помогает студентам говорить мягче.
  = The construction helps students speak more gently.

Говорить is imperfective, so it fits a general skill or habitual action:

• helps you speak more gently and precisely

This is about how you speak in general, not one single completed utterance.

If you used сказать, it would sound more like helping someone say one particular thing.

They are comparative forms:

• мягче = softer / more gently
• точнее = more precise / more precisely

In this sentence they go with говорить, so in English they are best translated adverbially:

• говорить мягче и точнее
  = to speak more gently and more precisely

A useful thing to remember: in Russian, the comparative form is often the same for both adjectives and adverbs.

Because the sentence is referring to the expression itself as a piece of language.

English might use quotation marks like this:

• the construction “not exactly ..., but ...”

Russian normally uses angle quotes:

• «...»

So конструкция «не то чтобы ..., но ...» means the construction not exactly ..., but ...

A very common pattern is:

Не то чтобы X, но Y.

Examples:

• Не то чтобы я устал, но хочу отдохнуть.
  = It’s not exactly that I’m tired, but I want to rest.

• Не то чтобы фильм плохой, но он скучноват.
  = It’s not that the film is bad, but it’s a bit boring.

• Не то чтобы она злая, но бывает очень резкой.
  = It’s not exactly that she’s mean, but she can be very sharp.

This is why your sentence says the construction helps you speak more gently and more precisely: it lets you express nuance instead of making a blunt statement.