INP metric: Too many spans with <unknown> target due to disappearing DOM elements

### Problem Statement

We are seeing a large number of INP-related spans where the clicked element is reported as ``.
This happens when the user clicks UI elements that immediately disappear from the DOM right after the interaction — most commonly:

- closing buttons (e.g., closing a modal),
- clearing input with an “X” button,
- removing items from lists, cards, etc.

Because these elements are removed, by the time Sentry processes the INP event, `e.target` is already `null`, which results in spans showing `` instead of the actual clicked element.
This significantly reduces the usefulness and traceability of INP measurements.

### Solution Brainstorm

A potential fix is to capture and cache metadata about the clicked element at the moment of the click event — before the element disappears.

Example approach:

1. On click, immediately compute and store the result of `htmlTreeAsString(event.target)` (or an equivalent helper used for INP).
2. When constructing INP spans, use the cached `htmlTreeAsString` value instead of trying to read `event.target` again (which may already be null after DOM removal).

### Product Area

Unknown