[Bug]: Tooltip and Dropdown anchoring not working

Component

Tooltip

Package version

3.0.1

@microsoft/fast-element version

?

Environment

System:
    OS: Linux 5.0 undefined
    CPU: (8) x64 Intel(R) Core(TM) i9-9880H CPU @ 2.30GHz
    Memory: 0 Bytes / 0 Bytes
    Shell: 1.0 - /bin/jsh
  npmPackages:
    @fluentui/web-components: 3.0.1 => 3.0.1

Current Behavior

Tooltip and dropdown do not work together. When applying a tooltip to the dropdown the tooltip appears at the top-left of the screen.

I believe the issues is related to the way these two components handle css positioning anchoring. The dropdown will give itself an anchor-name in order to coordinate with the listbox popover:

https://github.com/microsoft/fluentui/blob/e8033487274728d29528055e3aadf6c75e65e4cc/packages/web-components/src/dropdown/dropdown.base.ts#L257

However, the tooltip also needs a stable anchor name:
https://github.com/microsoft/fluentui/blob/e8033487274728d29528055e3aadf6c75e65e4cc/packages/web-components/src/tooltip/tooltip.ts#L111

I believe the issue is that the tooltip initializes and captures the current anchor-name, then the dropdown changes it's anchor-name later.

Expected Behavior

The tooltip should be positioned next to the dropdown.

Reproduction

https://stackblitz.com/edit/vitejs-vite-ygrqqvpa

Steps to reproduce

Hover over the dropdown in the example, the tooltip appears in the top-left.

Are you reporting an Accessibility issue?

no

Suggested severity

High - No workaround

Products/sites affected

Fabric UX

Are you willing to submit a PR to fix?

yes

Validations

• Check that there isn't already an issue that reports the same bug to avoid creating a duplicate.
• The provided reproduction is a minimal reproducible example of the bug.