Query parser migration

Created by: rvantonder

This task tracks query parser migration to the new parser. Checklist of items to do:

• Differential testing of search inputs and internal representation (build a corpus of inputs and convert them using both parsers, check that the results are equivalent). Bugs fixed:
  • #12572
  • #12733 (closed)
• Run search-integration-tester test cases https://github.com/sourcegraph/sourcegraph/pull/13004
• Add /.../ syntax or deprecate it. The new parser doesn't support it yet, but it may be a fair decision to just drop support.
• Document the configuration/settings that control parsing, esp. for fallback.
• fix alertForOverRepoLimit for queries containing and/or #13125 (closed)