[docs-Infra] Update indexName to 'material-ui-v6' for V6 Search

[dav-is]

Uses a separate index based on https://v6.mui.com/

Adds a new crawler that crawls once a month.

Fix: https://github.com/mui/material-ui/issues/45771

• [x] I have followed (at least) the PR section of the contributing guide.

[mui-bot]

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[Janpot]

Approving, although I think this should be a variable so that we can update it without requiring code changes

[ZeeshanTamboli]

@dav-is Maybe you want to merge this PR. It has been open for a while.