Start Using BeginSignIn command and remove obsolete API command calls (Take 2)

[yuwenmemon]

@robertjchen please review

Second try of #10222

Details

Start using the BeginSignIn command added in https://github.com/Expensify/Web-Expensify/pull/34408

Fixed Issues

$ https://github.com/Expensify/Expensify/issues/218743

Tests

1. Do a normal sign-in flow for a user that already has a validated account, make sure it works properly:
   https://user-images.githubusercontent.com/4741899/182488142-8044224b-396a-46b2-97a2-69599c0ee76d.mp4

---

1. With the same account do the same sign in. Click "Forgot?" on the password form.

2. Make sure you see the following:
   

3. And that you get send a password reset link email.

4. Click the "Resend link" button.

5. Make sure you get another email

---

1. Sign in with an email that DOES NOT already have an account

2. Make sure that right away you see:
   

3. ...And that you get an email with a sign-in link:

4. Before validating that account by clicking the link in the email, sign-in with that account again, make sure that you get an email with a sign-in link again.

---

1. Sign-in with a phone number that does not have an account yet, make sure you see the following:
   

2. And that you get a text message with your magic sign-in link:
   

---

Error handling:

1. Sign in with a number that is not actually a phone number, make sure you get the following error message:

2. Sign in with a login that is not actually an email, make sure you get the following error message:

[melvin-bot]

Looks like you modified deprecatedAPI.js! To be clear, you should not be adding any code to this file.

Instead, all new API commands should use API.js, and follow our guidelines for writing new API commands.

Unsure if your change is okay? Drop a note in #expensify-open-source!

[robertjchen]

LGTM! 👍

[melvin-bot]

@yuwenmemon looks like this was merged without passing tests. Please add a note explaining why this was done and remove the Emergency label if this is not an emergency.

[OSBotify]

✋ This PR was not deployed to staging yet because QA is ongoing. It will be automatically deployed to staging after the next production release.

[iwiznia]

Just saw this randomly. This is wrong, this is a string that should be localized. Can you send a PR to fix that please?

[yuwenmemon]

Do you have a link for the context for this? These updates to errors have been breakneck - I want to make sure I have everything straight.

[yuwenmemon]

Oh, wait I see it. Yeah, my bad, updating!