[Weighted Routing] Allow search with custom string on weighed in nodes

[anshu1106]

Is your feature request related to a problem? Please describe.
#5873 adds support to disallow searches with preference parameter with strict weighted shard routing. On a deep dive we found that searches with custom_string helps in building shard caches across requests and Open Search dashboard extensively use this feature. Disallowing this feature entirely can affect search latencies as well.

Describe the solution you'd like
Support searches with custom string to return shard routings present in weighed in nodes. This way weighted routing is honoured and search performance is not affected. Searches targeting specific nodes PREFER_NODES, LOCAL, ONLY_LOCAL, ONLY_NODES are still not allowed.

Describe alternatives you've considered
A clear and concise description of any alternative solutions or features you've considered.

Additional context
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