[8.x] fix: [Search:AppSearch:Engines page]Incorrect total number of o…

…ptions announced for Join our user research... combo box (elastic#200567) (elastic#201198)

# Backport

This will backport the following commits from `main` to `8.x`:
- [fix: [Search:AppSearch:Engines page]Incorrect total number of options
announced for Join our user research... combo box
(elastic#200567)](elastic#200567)

<!--- Backport version: 9.4.3 -->

### Questions ?
Please refer to the [Backport tool
documentation](https://github.com/sqren/backport)

<!--BACKPORT [{"author":{"name":"Alexey
Antonov","email":"[email protected]"},"sourceCommit":{"committedDate":"2024-11-21T14:12:42Z","message":"fix:
[Search:AppSearch:Engines page]Incorrect total number of options
announced for Join our user research... combo box (elastic#200567)\n\nCloses:
elastic#200542\r\n\r\n## Description\r\nVisible total number of options should
the same as announced for the\r\nuser as not to confuse them. Especially
for the users using assistive\r\ntechnologies.\r\n\r\n## What was
changed: \r\n1. `EuiSelect`.`hasNoInitialSelection` attribute should be
set to true\r\nonly in case of no default
value.","sha":"c145ba1bbc9c47e06d712792d0cd3dcb08fc5218","branchLabelMapping":{"^v9.0.0$":"main","^v8.18.0$":"8.x","^v(\\d+).(\\d+).\\d+$":"$1.$2"}},"sourcePullRequest":{"labels":["Project:Accessibility","release_note:skip","v9.0.0","Team:Search","backport:prev-minor"],"title":"fix:
[Search:AppSearch:Engines page]Incorrect total number of options
announced for Join our user research... combo
box","number":200567,"url":"https://github.com/elastic/kibana/pull/200567","mergeCommit":{"message":"fix:
[Search:AppSearch:Engines page]Incorrect total number of options
announced for Join our user research... combo box (elastic#200567)\n\nCloses:
elastic#200542\r\n\r\n## Description\r\nVisible total number of options should
the same as announced for the\r\nuser as not to confuse them. Especially
for the users using assistive\r\ntechnologies.\r\n\r\n## What was
changed: \r\n1. `EuiSelect`.`hasNoInitialSelection` attribute should be
set to true\r\nonly in case of no default
value.","sha":"c145ba1bbc9c47e06d712792d0cd3dcb08fc5218"}},"sourceBranch":"main","suggestedTargetBranches":[],"targetPullRequestStates":[{"branch":"main","label":"v9.0.0","branchLabelMappingKey":"^v9.0.0$","isSourceBranch":true,"state":"MERGED","url":"https://github.com/elastic/kibana/pull/200567","number":200567,"mergeCommit":{"message":"fix:
[Search:AppSearch:Engines page]Incorrect total number of options
announced for Join our user research... combo box (elastic#200567)\n\nCloses:
elastic#200542\r\n\r\n## Description\r\nVisible total number of options should
the same as announced for the\r\nuser as not to confuse them. Especially
for the users using assistive\r\ntechnologies.\r\n\r\n## What was
changed: \r\n1. `EuiSelect`.`hasNoInitialSelection` attribute should be
set to true\r\nonly in case of no default
value.","sha":"c145ba1bbc9c47e06d712792d0cd3dcb08fc5218"}}]}]
BACKPORT-->

Co-authored-by: Alexey Antonov <[email protected]>

x-pack/plugins/enterprise_search/public/applications/app_search/components/app_search_gate/app_search_gate.tsx

@@ -558,7 +558,7 @@ export const AppSearchGate: React.FC = () => {
           )}
         >
           <EuiSelect
-            hasNoInitialSelection
+            hasNoInitialSelection={participateInUXLabs === null}
             options={[
               {
                 text: i18n.translate(

x-pack/plugins/enterprise_search/public/applications/workplace_search/views/overview/gated_form.tsx

@@ -649,7 +649,8 @@ export const WorkplaceSearchGate: React.FC = () => {
           )}
         >
           <EuiSelect
-            hasNoInitialSelection
+            data-test-subj="enterpriseSearchWorkplaceSearchGateSelect"
+            hasNoInitialSelection={participateInUXLabs === null}
             options={[
               {
                 text: i18n.translate(