[Extensions] Promisify chrome.devtools.network namespace

Before this commit, methods in the chrome.devtools.network namespace and
the Request object (specifically getHAR and getContent) were limited to
callback-based interaction.

After this commit, network.getHAR and Request.getContent are
promisified. They return a Promise when called without a callback. Unit
tests now cover these methods, ensuring they correctly handle responses
from the ExtensionServer.

This was accomplished by applying the promisification pattern to the
network-related implementations in ExtensionAPI.ts and updating the
associated declaration and test files.

*Note* since I'm not a Typescript expert I used Gemini to help write
this. Any feedback on a simpler or more readable solution is welcome.

Bug: 496604552, 496604551, 496616808
Change-Id: I2be23a77aeefaf06e26b57dfe01490b0ab5c164c
TAG=agy
Reviewed-on: https://chromium-review.googlesource.com/c/devtools/devtools-frontend/+/7802275
Auto-Submit: Justin Lulejian <jlulejian@chromium.org>
Reviewed-by: Danil Somsikov <dsv@chromium.org>
Commit-Queue: Danil Somsikov <dsv@chromium.org>
Reviewed-by: Philip Pfaffe <pfaffe@chromium.org>