There were many occasions where the designs didn't adhere to the figma. This PR intends to fix most of those cases.

For reviewers:

• Design (@rrhyne): Check out the screenshots
• Cody Prime (probably @taras-yemets): I suggest you go commit by commit for extra clarity.
• Front-end devs (@sourcegraph/frontend-devs): You only need to check https://github.com/sourcegraph/sourcegraph/pull/63244/commits/af5371751ea33facd6f7bd78c46305d9c9a37dc4. and maybe https://github.com/sourcegraph/sourcegraph/pull/63244/commits/816d1781917500cb18879f0eb4594bb29033e717 to see the usages of the new utility classes. WDYT about the "3c" naming? I wanted to use something like "3.25", but sadly, Tailwind didn't allow . there. I could call it 3-25, or get rid of it altogether if you say it's a terrible idea, but I already had to use the new, 1.125rem = 18px space at 6 places, and @rrhyne uses it a lot in the Figma so I suspect we'll need it at a bunch more places, so would be nice to have that utility class available.

This PR does three things:

1. Fixes https://github.com/sourcegraph/sourcegraph/issues/63038

2. Fixes https://github.com/sourcegraph/sourcegraph/issues/63245

3. Does most of https://github.com/sourcegraph/sourcegraph/issues/63039, although not perfect.

I chose to create this PR early despite everything being 100% there with the design changes for three reasons:

1. To surely ship my progress before my parental leave
2. To avoid big conflicts with other PRs (I already have another one under review that conflicts with this at a few places)
3. To help @taras-yemets use the new utility classes at other places.

Test plan

All low-risk changes.
I did manual QA.
See the screenshots.