feat(gax): Migrate from retry-request to gaxios for retry functionality

[mbrjo]

Summary

The gax package still depends on retry-request, which has been deprecated since July 2024. The deprecation notice in the original repository states:

THIS REPOSITORY AND PACKAGE WILL BE DEPRECATED IN JULY 2024. RELEVANT FUNCTIONALITIES HAVE BEEN MOVED TO GOOGLEAPIS/GAXIOS

Since both retry-request and gaxios are now maintained in this monorepo, it would be beneficial to migrate gax to use gaxios for retry functionality.

Current State

• gax@5.0.6 (latest stable) depends on retry-request@^8.0.0
• gax@6.0.1-experimental still depends on retry-request@^8.0.0
• retry-request was migrated to this monorepo in PR chore: Retry request migration #858, but not removed from gax

Impact

All downstream packages (@google-cloud/kms, @google-cloud/storage, etc.) inherit this deprecated dependency, which may cause concerns for users running security audits on their dependencies.

Suggested Solution

Migrate the retry logic in gax to use gaxios instead of retry-request, then deprecate/remove the retry-request package from this monorepo.

[feywind]

@mbrjo Thanks for the issue! I think you're probably right, but it may have to wait a bit behind some other work.