As per https://github.com/matrix-org/matrix-doc/issues/1354

This is whitelisted to only jitsi widgets for now as per comment,
mostly because any widget that we may make always-on-screen we need
to preemptively put in a PersistedElement container, which is
unnecessary for any other widget.

Apologies that this does a bunch of refactoring which could have
been split out separately: I only discovered what needed to be
refactored in the process of doing this.

Fixes element-hq/element-web#6984

Turns out the z-index was to make the avatar appear above the
EventTile_line even though it comes before in the DOM (it's
absolutely positioned to overlap with it). Instead, just put
it afterwards in the DOM.