Deprecate public-provider command

[shenglol]

Closes #14376.

Microsoft Reviewers: Open in CodeFlow

[github-actions]

Test this change out locally with the following install scripts (Action run 9765361803)

VSCode

• Mac/Linux

  bash <(curl -Ls https://aka.ms/bicep/nightly-vsix.sh) --run-id 9765361803

• Windows

  iex "& { $(irm https://aka.ms/bicep/nightly-vsix.ps1) } -RunId 9765361803"

Azure CLI

• Mac/Linux

  bash <(curl -Ls https://aka.ms/bicep/nightly-cli.sh) --run-id 9765361803

• Windows

  iex "& { $(irm https://aka.ms/bicep/nightly-cli.ps1) } -RunId 9765361803"

[github-actions]

Dotnet Test Results

    72 files   -     35      72 suites   - 35   23m 2s ⏱️ - 8m 22s
10 932 tests  -     24  10 932 ✅  -     23  0 💤  - 1  0 ❌ ±0 
25 760 runs   - 12 888  25 760 ✅  - 12 885  0 💤  - 3  0 ❌ ±0 

Results for commit ca40aa9. ± Comparison against base commit 888a9f9.

♻️ This comment has been updated with latest results.