feat(global-frontend): keep sessionless conversations on one pool - #17886

PR issue link: missing

Every PR needs a linked issue so the work is traceable to a tracked task.
Link one of the following and re-run the check (editing the PR description re-triggers it):

• A Linear issue, for example Closes DYN-1234 in the description, or the
  issue ID in the branch name (user/dyn-1234-description).
• A GitHub issue: Fixes #123 to close it, or a non-closing form like
  Part of #123 for an issue that outlives the PR. Issues in sibling
  repositories in the org count too, for example
  ai-dynamo/enhancements#12.

If no issue exists yet, create one first and start the work from it.
This check is required: release/1.7.0 has been cut.