The password along with username is normally saved and updated on a redirect. In that case the username is picked up correctly. However, in case of "suggest password" the password is actually remembered in advance, during this action, not during redirect. Because of your fiddle does not provide correct redirect, after first "suggest password" attempt, credentials are saved as a password with "no username".

This "no username" is the reason for immediate pop-up during second "suggest password" attempt because Chrome can't decide which username is correct - "no username" or that one you filled up in the form. Note that second, "correct one" is pickable in the "Username" field too - its triangle is visible on your screenshot. The reason for immediate pop-up is the same as it was for first attempt - Chrome wants to save suggested password in advance and does not wait a redirect. The reason why Chrome remembers suggested password right away and doesn't remember username in the same moment is that suggested password is trusted upon form submission but the username is not.

It seems like Edge and Firefox have the same behavior.

Solution for productive sites: implicitly provide correct redirect (or substitutive actions). Solution for users: delete saved credentials with blank username for that sites where a username should exist.

"Suggest strong password" is available on Chrome for Android as explained here:

When you want to generate a secure password:

1. Turn on sync in Chrome.
2. Go to a website and sign up for an account.
3. Tap on the password text box.
4. Tap Suggest strong password.
   • If you don't see this option, tap Password Save your password and then Suggest strong password.
5. You'll see a preview of the password. To confirm, tap Use password.
6. Finish signing up for your account. Your password is automatically saved to Chrome.

However, there is an issue with newer versions of Chrome that does not allow the suggestion to appear as testified here or here by many. As suggested on those links, removing the Chrome updates allows the suggestion message to appear.

On the left, when I uninstalled Chrome updates, on the right Chrome's latest version

Suggested pasword on old version

You can also try to change your autofill service as suggested on one of the posted links.

Or you just wait for future versions to fix the issue.

First of all, StackExchange is not a place for product recommendations. There are plenty of password managers, both free and paid, that can be found on the internet. I want to focus specifically on the password storage functionality of Google as you asked.

I want to give a compliment to you recognizing your security can be improved, which is also core to your question: The Google password storage is better then your current method (based on the CIA triad) because of the following:

• Your passwords are encrypted (confidentiality)
• You have online access and synchronized access to your passwords (availability)
• Google Password Storage has better options to monitor changes to your passwords (integrity)

The Google password storage has everything you were looking for in the first place. It is secure, it is able to synchronize between devices, you can view passwords at your own discretion and the functionality is completely free. I think your question is more about how secure it actually is, maybe even in comparison to other password managers.

Just like with 'regular' password managers, you need a master key to access your password storage. In this case you will need access to your Google account. I would strongly advice you to use 2FA and a strong master password (length is most important) to secure your account. When you turn synchronization on, your passwords will be saved to your Google account. When you do not have synchronization on, your passwords will be saved locally.

Let me get one thing straight from one of the questions you linked: A password in a password manager is not hashed but encrypted, because of the very nature of the functionality of a password manager. You need to be able to see and use a password and therefor it cannot be hashed. This is the same for all password managers, including the Google password storage.

The other question you linked is only applicable to passwords being saved locally, something you don't have to worry about because your passwords will be saved in your Google account as mentioned above.

Although the risks explained in the answer of ShayanKM are true, your critical risk is your Google account. as long as you protect your account well enough there should not be a lot of risk in using the Google password storage compared to other password managers. The only real difference might be that you could want to prefer open source password managers, which Google password storage is not. I will leave it up to you to decide if this is important.

There are other issues that are not specific to Google, such as vulnerabilities being found in the software or not securing your device. Remember that password managers don't have to be perfect, they have to be better then not having one.

Based on chromium; this should work : (the suggest password comes after already known passwords for that site)

<form id="login" action="signup.php" method="post">
  <input type="text" autocomplete="username">
  <input type="password" autocomplete="new-password">
  <input type="password" autocomplete="new-password">
  <input type="submit" value="Sign Up!">
</form>

more examples : https://www.chromium.org/developers/design-documents/form-styles-that-chromium-understands