@MNguyen, @violetto, @vshchepakina
Created this page and here is the screenshot.
If no problem I will update the code soon.
Also, in the toolbar, Login / Register is ok?

Updated new login page.
Click Forgot password? will switch the page content to password recovery form, and stay in the same page.
Click Back to login will switch the login and register forms back.
The reason is, I did not find a way to add a separated sub page for password form under link store.wikimedia.org/account.
Also modified toolbar entrance for login and register as Login.

@vshchepakina we wanted just "Join" on the menu bar right?

@HuiZSF, on the "Forgot password?" I wonder if we can change the form instead of going to another page? For example,

Currently in the "Login" form, you have:

Login
_ _

Email Address
(Field)

Password - Forget Password
(Field)

[Login button]

When you click on "Forget Password," the form becomes (without going to another page)

Forgot your password?
_ _

Email Address
(Field)

[Submit button]
[Back to login link]

@violetto
The 3 forms are actually on the same page now, but visually separated to 2 pages.

I will change the behavior of "Forgot password page".
When click "Forgot your password", "login form" will be replaced by "forgot password form", visually on the same page.

Nice!!

Updated.
Now the login form and password recover form will alternatively appear in the exactly same position.

Yaaaaay what an improvement! Thanks for your hard work, @HuiZSF!
If you could add some minor changes, it will be perfect!

1. Capitalize where needed: Recover Password, Back to Login (omit 'or).
2. Give the button / 'Back to Login' some breathing room: 1.5em
3. Resize 'Back to Login' text to same size as 'Submit', should be 1em

@MNguyen
Updated. Thank you :)

Yes! It looks great! Thanks for being so quick also. Can you sign off on this @violetto?