Are you actually asking for alignment or for direction?

I'm asking for alignment. I think we already have direction support in VE - under language selection (my last screenshot).

The direction is set inline (<span>) and not on a block (<p> or <div>). For scenarios that you've described, it would make more sense to set direction and not alignment. The alignment would be set automatically according to the direction.

It's true that it's available in common word processors like Microsoft Word and Google Docs, but are they actually used there frequently? And what semantic roles can they have in wikis?

I am not saying that there are no such semantic roles. There probably are. For example, you could display quotations from books or section summaries like this. It's often convenient to align numbers to the right, especially in tables. To actually do such things now, there is no wikitext, and Visual Editor buttons usually map to wikitext constructs and not to HTML (the language button is an exception to that, and I'm not so happy about it). It's possible to define alignment on wiki pages today, but you have to do it with actual HTML and CSS, and it's often wrapped in a template. The template is often the thing that makes the content semantic, at least in how the editors perceive it.

So I would first think of specific semantic scenarios where a different alignment would be needed, and then think about adding them to the toolbar.

(To clarify: The comment above is just my thinking about it, and it's based on my editing experience in wikis and in word processors. I'm not a decision-maker when it comes to Visual Editor. I'll leave more professional comments to real designers and product managers.)

I use them frequently on word and needs them on the VE as well.
The senario is common on the further reading section when recommending materials in two languages.

In T288390#7278020, @Orlysi wrote:

I use them frequently on word and needs them on the VE as well.
The senario is common on the further reading section when recommending materials in two languages.

This is indeed often necessary when writing in Hebrew (or another RTL language) and having to quote something in English (or another LTR language). But what you actually need to change is language and direction and not alignment. Even in Microsoft Word it's incorrect to use the alignment button for this, and you should use the direction button instead. It looks like ¶▶. You can also use the the left-hand Ctrl-Shift keys on the keyboard as a shortcut.

In the Hebrew Wikipedia, there's the {{ltr}} template for this for general text. I wish it was integrated directly into Visual Editor as a toolbar button, but it currently isn't. For references, there's something more structured that Eran worked on in wikitext, but I don't think it's properly integrated with Visual Editor, and it definitely should be. Eran, you probably know what I am talking about, can you please remind us what's the status of that?

Actually the best solution might be to creat a ribbon bottom that offers you the two options relating to multi language editing.

Ref supports dir parameter since T15673 but we didn't expose it to VE

In T288390#7278098, @eranroz wrote:

Ref supports dir parameter since T15673 but we didn't expose it to VE

Is there a task for that? There should be.