Trim down extensions `ci-build.ps1` script

The `ci-build.ps1` scripts used for building our azd extensions can be trimmed down/simplified:

https://github.com/Azure/azure-dev/blob/main/cli/azd/extensions/microsoft.azd.demo/ci-build.ps1
https://github.com/Azure/azure-dev/blob/main/cli/azd/extensions/microsoft.azd.ai.builder/ci-build.ps1
https://github.com/Azure/azure-dev/blob/main/cli/azd/extensions/microsoft.azd.extensions/ci-build.ps1

To consider:

- [ ] ~~Unused `[string] $MSYS2Shell` param (_Originally posted by @richardpark-msft in https://github.com/Azure/azure-dev/pull/5733#discussion_r2356195195_)~~ (see comment below)
- [ ] Depending on the Go version we use, `$env:GOEXPERIMENT = "loopvar"` can be omitted ( _Originally posted by @richardpark-msft in [#5733](https://github.com/Azure/azure-dev/pull/5733/files#r2356198988)_)
- [ ] Document `$BuildRecordMode` or remove if irrelevant for extensions ( _Originally posted by @richardpark-msft in [#5733](https://github.com/Azure/azure-dev/pull/5733/files#r2356203396)_)