fix(docker): missing permissions to start docker (backport release-3.6.x)

[loki-gh-app]

Backport 39d2bea from #19947

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What this PR does / why we need it:

With the latest release, the docker container is failing to start up because of missing permissions.

We need to update the docker file to copy the binaries with the right permissions for the user.

Which issue(s) this PR fixes:
Fixes #19904

Special notes for your reviewer:

Before this change starting the docker compose was failing with missing permissions.
As we have an intermediate step we need to copy the binaries with the right permissions or the docker will fail to start.

To reproduce:

• get the latest version and try to start docker compose will fail
• After this change, docker compose should start as expected

Checklist

• Reviewed the CONTRIBUTING.md guide (required)
• Documentation added
• Tests updated
• Title matches the required conventional commits format, see here
  • Note that Promtail is considered to be feature complete, and future development for logs collection will be in Grafana Alloy. As such, feat PRs are unlikely to be accepted unless a case can be made for the feature actually being a bug fix to existing behavior.
• Changes that require user attention or interaction to upgrade are documented in docs/sources/setup/upgrade/_index.md
• If the change is deprecating or removing a configuration option, update the deprecated-config.yaml and deleted-config.yaml files respectively in the tools/deprecated-config-checker directory. Example PR

[ToxicLand]

Just updated to 3.6.1, but the issue still persists.

2025-11-21T17:08:27.089161571Z mkdir /loki/chunks: permission denied
2025-11-21T17:08:27.089200528Z error creating object clien
2025-11-21T17:08:27.089291583Z level=error ts=2025-11-21T17:08:27.087829621Z caller=log.go:223 msg="error running loki" err="mkdir /loki/chunks: permission denied\nerror creating object client\ngithub.com/grafana/loki/v3/pkg/storage.(*LokiStore).chunkClientForPeriod\n\t/src/loki/pkg/storage/store.go:241\ngithub.com/grafana/loki/v3/pkg/storage.(*LokiStore).init\n\t/src/loki/pkg/storage/store.go:201\ngithub.com/grafana/loki/v3/pkg/storage.NewStore\n\t/src/loki/pkg/storage/store.go:193\ngithub.com/grafana/loki/v3/pkg/loki.(*Loki).initStore\n\t/src/loki/pkg/loki/modules.go:902\ngithub.com/grafana/dskit/modules.(*Manager).initModule\n\t/src/loki/vendor/github.com/grafana/dskit/modules/modules.go:136\ngithub.com/grafana/dskit/modules.(*Manager).InitModuleServices\n\t/src/loki/vendor/github.com/grafana/dskit/modules/modules.go:108\ngithub.com/grafana/loki/v3/pkg/loki.(*Loki).Run\n\t/src/loki/pkg/loki/loki.go:549\nmain.main\n\t/src/loki/cmd/loki/main.go:130\nruntime.main\n\t/usr/local/go/src/runtime/proc.go:283\nruntime.goexit\n\t/usr/local/go/src/runtime/asm_amd64.s:1700\nerror initialising module: store\ngithub.com/grafana/dskit/modules.(*Manager).initModule\n\t/src/loki/vendor/github.com/grafana/dskit/modules/modules.go:138\ngithub.com/grafana/dskit/modules.(*Manager).InitModuleServices\n\t/src/loki/vendor/github.com/grafana/dskit/modules/modules.go:108\ngithub.com/grafana/loki/v3/pkg/loki.(*Loki).Run\n\t/src/loki/pkg/loki/loki.go:549\nmain.main\n\t/src/loki/cmd/loki/main.go:130\nruntime.main\n\t/usr/local/go/src/runtime/proc.go:283\nruntime.goexit\n\t/usr/local/go/src/runtime/asm_amd64.s:1700"