Learn Hardcore Portuguese (Brazil): É importante que você seja organizado no trabalho. - It is important that you be organized at work.

Because after É importante que... Portuguese normally requires the present subjunctive to express a recommendation/necessity/importance rather than a statement of fact.

que você seja = “that you be” (subjunctive, desired/required)
If you used é/está, it would sound like you’re stating a fact about the person, not expressing what’s important:
É importante que você é organizado → generally considered incorrect/nonstandard in Portuguese.
É importante que você esteja organizado could work in some contexts, but it changes the nuance (see below).

What’s the grammar behind É importante que...?

É importante is an impersonal expression (like “It’s important”) followed by a clause introduced by que. This structure commonly triggers the subjunctive:

É + adjective (importante, necessário, bom, melhor, estranho, etc.) + que + subjunctive

Is você formal or informal here? Could I say tu?

In Brazil, você is very common and often neutral (it can be informal or polite depending on tone and region).
You can use tu in regions where it’s common, but then the verb form changes:

É importante que tu sejas organizado no trabalho. (standard tu
- sejas)
  In many Brazilian regions, people say tu but still conjugate like você (colloquial):
É importante que tu seja organizado... (common in speech in some places, but not formal writing)

Why is it organizado and not organizada?

The adjective agrees with the person being addressed.

If you’re speaking to a man (or using masculine as default), organizado.
If you’re speaking to a woman, organizada:
É importante que você seja organizada no trabalho.
For a group, you’d use plural:
vocês sejam organizados/organizadas

Does ser organizado mean a permanent trait? What about estar organizado?

Often, yes: ser + adjective tends to describe a characteristic/quality (being an organized person).
estar organizado tends to describe a more temporary state (being organized at the moment / having things in order).
So:

seja organizado = “be organized (as a habit/behavior expectation)”
esteja organizado = “be organized (right now / in your current situation),” e.g., before an audit or presentation.

What does no trabalho literally mean, and why is it no?

no is a contraction of em + o:

em = “in/at”
o = “the”
So no trabalho = em o trabalho → “at work / in the workplace.”
Similarly:
na escola = em + a
nos EUA = em + os

Could I say no seu trabalho or no ambiente de trabalho instead?

Yes, and each has a slightly different feel:

no trabalho = “at work” (general, very natural)
no seu trabalho = “in your job / in your work (specifically yours)” (more personal/specific)
no ambiente de trabalho = “in the work environment/workplace” (more formal, broader)

Why is the word order É importante que você seja organizado and not Você é importante...?

Because the sentence is built around an impersonal evaluation: É importante (“It’s important”) + a clause explaining what is important.
If you said Você é importante, you’d be saying You are important, which changes the meaning entirely.

Can I omit que?

Not in this structure. que is needed to connect the main clause (É importante) to the subordinate clause (você seja...).
You can restructure the sentence to avoid que, but then you’d change the form:

É importante ser organizado no trabalho. (“It’s important to be organized at work.”)

How is this sentence typically pronounced in Brazilian Portuguese?

A common Brazilian pronunciation (rough guide) is:

É like “eh”
importante ≈ im-por-TAHN-chee (final e often sounds like -chi in many accents)
que often sounds like kee
você ≈ vo-SEH (with the stress on -cê)
seja ≈ SEH-jah
organizado ≈ or-ga-nee-ZAH-doo (final o often sounds like -oo)
trabalho ≈ tra-BAH-lyoo (the lh is like the lli in “million”)