Automate Non-functional Tests

[mpstefan]

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After completing our manual non-functional testing and documenting the process, we should proceed to automate our non-functional tests so they do not incur additional toil on the release process.

The below stories are linked to a manual non-functional test. Each test should be automated to the point where a script can be manually ran to execute the test.

### Tasks
- [ ] https://github.com/nginxinc/nginx-gateway-fabric/issues/1364
- [ ] https://github.com/nginxinc/nginx-gateway-fabric/issues/1365
- [ ] https://github.com/nginxinc/nginx-gateway-fabric/issues/1367
- [ ] https://github.com/nginxinc/nginx-gateway-fabric/issues/1368
- [ ] https://github.com/nginxinc/nginx-gateway-fabric/issues/1369
- [ ] https://github.com/nginxinc/nginx-gateway-fabric/issues/1366
- [ ] https://github.com/nginxinc/nginx-gateway-fabric/issues/1286
- [ ] https://github.com/nginxinc/nginx-gateway-fabric/issues/1435
- [ ] https://github.com/nginxinc/nginx-gateway-fabric/issues/1901