EREGCSC-2685 -- Move subject page search box to filter region (#1461)

* feat: move search input on subjects page; direct to search page when used

* feat: method to get subject name as input placeholder

* feat: styles; use v-input label instead of placeholder

because placeholder does not allow text-overflow: ellipsis

* style: various style tweaks

* fix: counts based on q on search page and subjects param on subj pg

* test: fix a few failing tests

* chore: remove q param from subjects page logic

* chore: clean up vestigial logic concerning search query labels in subjects pg

* test: linting; begin updating subjects test suite

* test: fix a11y test and a few others

* test: update all subjects test to work without search query

* chore: remove search slot from policysidebar component

* style: tweak subjects page filters mobile styling

* chore: linting

* feat: refactor search input redirect/clear logic in subjects page

* test: clearing subjects input field should not reload page

* chore: tweak back button behavior

* style: tweak subjects page doc type selectors narrow styles

solution/ui/e2e/cypress/e2e/search.spec.cy.js

@@ -87,7 +87,7 @@ describe("Search flow", () => {
         cy.viewport("macbook-15");
         cy.visit(`/search`, { timeout: 60000 });
         cy.get("input#main-content")
-            .should("be.visible")
+            .should("exist")
             .type("test search", { force: true });
         cy.get('[data-testid="search-form-submit"]').click({
             force: true,
@@ -106,7 +106,7 @@ describe("Search flow", () => {
         });
 
         cy.get("input#main-content")
-            .should("be.visible")
+            .should("exist")
             .type("test", { force: true });
 
         cy.findByDisplayValue("test")
@@ -148,7 +148,7 @@ describe("Search flow", () => {
         });
 
         cy.get("input#main-content")
-            .should("be.visible")
+            .should("exist")
             .type(`${SEARCH_TERM_2}`, { force: true });
         cy.get('[data-testid="search-form-submit"]').click({
             force: true,
@@ -184,7 +184,7 @@ describe("Search flow", () => {
         });
 
         cy.get("input#main-content")
-            .should("be.visible")
+            .should("exist")
             .type(`${SEARCH_TERM}`, { force: true });
         cy.get('[data-testid="search-form-submit"]').click({
             force: true,