[BUG][Query enhancements] Discover state partially resets when switching between plugins

[joshuali925]

Describe the bug

When query enhancements is enabled, switching from Discover to Dashboard would set query language back to DQL, and switching back to Discover would reset the selected index pattern to the default one. This becomes problematic when there are no index patterns in the current workspace. It would show the previously selected dataset with an empty "SQL" query bar, but it is actually sending DSL requests to /internal/search/opensearch-with-long-numerals

To Reproduce
Steps to reproduce the behavior:

1. Create a new workspace with a opensearch connection. Ensure there are no index patterns in this workspace
2. Click on discover and select an index from the opensearch connection with SQL language
3. Run some query like SELECT request,response FROM apachelog where response = '501' limit 2
4. Click on Dashboards and click back to Discover
5. See index is still selected, language says "OpenSearch SQL", and query bar is empty
6. Now try to run the same SQL query, discover shows different results
7. In network tab, it calls POST /w/czLj6e/internal/search/opensearch-with-long-numerals instead of /w/czLj6e/api/enhancements/search/sql

Expected behavior
UI appearance and underlying state should be consistent

OpenSearch Version
main

Dashboards Version
main

Plugins

none

Screenshots

Notice SQL query is inside DSL

Host/Environment (please complete the following information):

• OS: [e.g. iOS]
• Browser and version [e.g. 22]

Additional context

One root cause is in setQuery,

OpenSearch-Dashboards/src/plugins/data/public/query/query_string/query_string_manager.ts

Lines 168 to 171 in 0be70a7

	public setQuery = (query: Partial<Query>) => {
	const curQuery = this.query$.getValue();
	let newQuery = { ...curQuery, ...query };
	if (!isEqual(curQuery, newQuery)) {

When there's no index pattern, on switching from Dashboard to Discover, it resets the query to default by passing query with dataset being undefined. The current logic will keep the original dataset in this case, but language still got reset to DQL. Now we have a index type dataset with incompatible language.

I've tried small effort fixes like

    if (!query.dataset) {
      newQuery.dataset = undefined;
    }

and the index is no longer selected, but clicking on "Run" still sends DSL queries to the apachelog index. Apparently there are more places causing issues and need to be fixed