Verify background-only network requests don't break on MV3

[twschiller]

Context

• Follow up to https://github.com/pixiebrix/pixiebrix-extension/issues/4357#event-7499863613
• We thing requests proxied via background page will keep the background page alive due to the open message
• However, we need to verify the background-only requests prior to releasing an MV3 extension
• So opening this issue as low priority just to track the concern

Background Activity

I think this cover most if not all of our concerns. If we do have truly-background activity, moving it to an offscreen document would be the right path.

I think all the pure background requests occur on start up or at a recurring interval (so restarts are OK), but I want to double-check as part of QA/verifying the MV3 build

• Starter Blueprints: on startup
• Deployment checks: startup and recurring intervals