Tests: Playwright test timeouts (#7231)

## Summary

See where we can use proper DOM waiting instead of waitForTimeout.

┆Issue is synchronized with this [Notion
page](https://www.notion.so/PR-7231-WIP-Playwright-test-timeouts-2c36d73d3650812b966ac3d9c338dfd4)
by [Unito](https://www.unito.io)

browser_tests/fixtures/components/SidebarTab.ts

@@ -116,7 +116,6 @@ export class WorkflowsSidebarTab extends SidebarTab {
   async switchToWorkflow(workflowName: string) {
     const workflowLocator = this.getOpenedItem(workflowName)
     await workflowLocator.click()
-    await this.page.waitForTimeout(300)
   }
 
   getOpenedItem(name: string) {
@@ -138,7 +137,6 @@ export class WorkflowsSidebarTab extends SidebarTab {
       .click()
     await this.page.keyboard.type(newName)
     await this.page.keyboard.press('Enter')
-    await this.page.waitForTimeout(300)
   }
 
   async insertWorkflow(locator: Locator) {