Cleanup and standardize badge colors in groups

[seisman]

Before

After

Updated badges:

• =>
• Update "DOI" to "Zenodo DOI". The "Zenodo DOI badge" reflects the concept DOI, not the DOI of the latest version, so it belongs to the 2nd group.

Newly added badges:

• 
• 

Removed badges:

• 
• 
• 
• 
• 

Closes #4768

Preview: https://github.com/GenericMappingTools/pygmt/blob/badges/README.md

[yvonnefroehlich]

Realy like the sorting of the badge by color.

[yvonnefroehlich]

Could we change "Contact" into "GMT Forum"?
(As this is not directly related to the badges, also fine with including this in another PR or in #4778.)

Suggested change

	[Documentation (development version)](https://www.pygmt.org/dev) | [Contact](https://forum.generic-mapping-tools.org) | [TryOnline](https://github.com/GenericMappingTools/try-gmt)
	[Documentation (development version)](https://www.pygmt.org/dev) | [GMT Forum](https://forum.generic-mapping-tools.org) | [TryOnline](https://github.com/GenericMappingTools/try-gmt)

[seisman]

See my comment https://github.com/GenericMappingTools/pygmt/pull/4776/changes#r3679209568. If we decide to remove the "Documentation (development version)" link, we may also want to remove the "Contact" and "TryOnline" link. So, let's revisit it separately.

[yvonnefroehlich]

I am wondering if it makes more sense to link to the latest version of the documentation, as it's likely not too many users install the dev version and update it over time.
(As this is not directly related to the badges, also fine with including this in another PR or in #4778.)

Suggested change

	[Documentation (development version)](https://www.pygmt.org/dev) | [Contact](https://forum.generic-mapping-tools.org) | [TryOnline](https://github.com/GenericMappingTools/try-gmt)
	[Documentation](https://www.pygmt.org/latest) | [Contact](https://forum.generic-mapping-tools.org) | [TryOnline](https://github.com/GenericMappingTools/try-gmt)

[seisman]

As mentioned in #4746 (comment), I have proposed to add a "Documentation" section in README.md, after which I feel the link is not longer necessary. So Let's revisit it later.