follow-up to #12203 add `No` button or `Do not ask again option` to show default browser dialog

Description

Default browser dialog prompt frequency may be too aggressive with asks on 2nd, 3rd, and 4th launches (and finally 8th and 20th launches). Consider adding a No button or Do not ask again as option to never ask again. Alternatively, could consider removing 3rd ask.

Steps to Reproduce

See test plan: https://github.com/brave/brave-core/pull/7716

Expected result:

“No” or “Never ask again” option, alternatively less frequent ask.

Reproduces how often:

Brave version (brave://version info)

Brave | 1.21.73

Version/Channel Information:

• Can you reproduce this issue with the current release? yes
• Can you reproduce this issue with the beta channel? yes
• Can you reproduce this issue with the nightly channel? yes

Other Additional Information:

• Does the issue resolve itself when disabling Brave Shields? n/a
• Does the issue resolve itself when disabling Brave Rewards? n/a
• Is the issue reproducible on the latest version of Chrome? n/a

Miscellaneous Information:

[davidgsd]

Do Brave developers really think people need to be asked nunerous times in a row, 8th, 20th etc. ad nauseum and presumably after every Brave update? This kind of assumption on the part of developers - that users are not savvy enough to decide by themselves which browsers they want to use and which they want to be the default without being asked 5 times will definitely become a self-fulfilling prophecy as savvier users look for other options, after wasting 15 minutes of their day to disable this ridiculous nag which apparently has no disable option in the settings. This is not user-friendly design. Thank you

[ocdtrekkie]

Removing the ability to disable default browser nags is vehemently anti-user, and shows a surprising choice to be more user hostile than Google manages to be.

The answer is simple: The same place in settings where the option to make it default exists, must also be a single option to disable it asking. Every other browser has this. Yours doesn’t. Fix it.