[code-infra] Fix playwright hash

[Janpot]

The cache key calculation is executed before packages are installed, and this always results in an empty file.
The --filter parameter is for filtering workspace packages this command operates on, not to filter listed packages. This command always returns an empty string. The cache key never changes. Thus we're always both downloading an old cache and re-installing playwright browsers.

I'm moving the cache handling steps after the install step and I'm changing the command to filter on installed packages only. It's the positional argument in pnpm list. I'm also removing --json as it's unnecessary and adding -r because playwright is not installed at the top level. It's not the most ideal (*) output but probably closest to what we want that is doable with a simple pnpm command.

I noticed restoring the cache takes as exactly long as running playwright install.

Current situation:

After the changes, we see the following numbers:

• Storing the cache takes about ~45s.
• Restoring the cache takes about ~22s
• Installing from cached takes about ~6s
• Installing from fresh takes about ~18s

In Circleci

• cache miss

  

• cache hit

  

In both cases this increases the CI time. I propose to remove the cache altogether. cc @mui/code-infra for your thoughts Superseded by #43881.

Also removing a dead CircleCi link

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(*) technically this output will invalidate a bit more often than strictly necessary, but we can probably live with it, no need to add extra complexity.

[mui-bot]

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[Janpot]

Superseded by #43880