docs: Add tweaks to the "Remote development" page (#12267)

Mostly tiny stuff. Quick run-down of the changes:
- Using `*Note*` instead of `NOTE` for the blockquote callouts
(piggybacking from https://github.com/zed-industries/zed/pull/11724)
- Use hyphens for bullet lists instead of asterisks
- Capitalize every (applicable) mention to Zed
- Capitalize mentions of other products (e.g., google cloud → Google
Cloud)
- Swap e.g. → for example — for clarity (latinisms may be unfamiliar for
some non-native English speakers, surprisingly!)

Release Notes:

N/A