Describe the bug:

We use an http proxy to communicate using the google-ads library. This worked fine on previous versions by setting the http_proxy and https_proxy env vars. When updating to 10.0.0 or later, I get the following error when using search:

         debug_error_string = "{"created":"@1620489718.036336118","description":"Failed to pick subchannel","file":"src/core/ext/filters/client_channel/client_channel.cc","file_line":5419,"referenced_errors":[{"
created":"@1620489718.036326964","description":"failed to connect to all addresses","file":"src/core/ext/filters/client_channel/lb_policy/pick_first/pick_first.cc","file_line":397,"grpc_status":14}]}"

This problem exists on 10.0.0 unmodified, 10.0.0 with PR 405 applied (with proxy set in yaml), and also on 11.0.0 unmodified. I am 100% sure that the grpc version is the same between working on google-ads 9.0.0 and failing on 10.0.0.

I've run a bisect which points at either 6c242d3, or the changes we had to make in our script to deal with the disruptive api changes. Do you have a more granular version of that commit that we could continue bisecting on?

Steps to Reproduce:
Internal build, sorry. I'm happy to test things to provide simplified versions or add debugging information as you'd like.

Expected behavior:
Proxy support continues to work.

Screenshots:
n/a

Library version and API version:

I see the failed call using /google.ads.googleads.v5.services.GoogleAdsService/Search

google-api-core 1.22.1
grpcio 1.37.1
google-ads 10.0.0 (or 11.0.0 if you'd rather)

Request/Response Logs:
I can generate these if you let me know what you're looking for.

Additional context:
n/a