This PR makes the initial steps at removing usage of the global Go HTTP
client, which was seen to have impacts on test flakiness in
https://github.com/coder/internal/issues/1020. The first commit removes
uses from tests, with the exception of one test that is tightly coupled
to the default client. The second commit makes easy/low-risk removals
from application code. This should have some impact to reduce test flakiness.
Zach