Migrate badge form to `GlFormFields`

What does this MR do and why?

Related to #435579 (closed)

Taking over a Community contribution that was not able to be finished - !139997 (closed)

I went down a few rabbit holes on this one and after going back and forth between implementations multiple times this is what I settled on. The previous version of validation didn't play very nicely with GlFormGroup which is why I ended up switching to GlFormFields for frontend validation. There were also a couple other bugs and technical debit that this MR fixes:

1. When editing a badge the modal would close even if there were validation errors
2. There was inModal prop that was not needed because we have isEditing prop. This form is only used in a modal when editing so we know it is in a modal when in edit mode. Guessing at one point it was used other places but that is not the case anymore.

MR acceptance checklist

Please evaluate this MR against the MR acceptance checklist. It helps you analyze changes to reduce risks in quality, performance, reliability, security, and maintainability.

Screenshots or screen recordings

Group new badge

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Required fields

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Invalid fields

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Group edit badge

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Screen_Recording_2024-08-09_at_2.15.18_PM	Screen_Recording_2024-08-09_at_2.10.17_PM

Project new badge

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Required fields

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Invalid fields

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Project edit badge

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Screen_Recording_2024-08-09_at_2.21.13_PM	Screen_Recording_2024-08-09_at_2.12.29_PM

How to set up and validate locally

1. Go to a group or project -> Settings -> General -> Badges
2. Click Add new badge
3. You can use something like http://gdk.test:3000/jashkenas/Underscore/badges/%{default_branch}/pipeline.svg for the Badge image URL field. Link can be a URL to anywhere (doesn't really matter for testing) and Name can be anything.