Better re-share experience

When I took a trace and tap "Share" button, perfetto generates link like https://ui.perfetto.dev/#!/?s=96c9XXXXX,
I can open that with other browsers. That UX is great, so far.

However, in that browser, address is just https://ui.perfetto.dev/#!/viewer?local_cache_key, that is not good because
- I cannot reshare it with others.
- if I reload the page, that just loads blank https://ui.perfetto.dev/#!/viewer?local_cache_key instead of the shared URL.
- If I open multiple perfetto tabs, no way to remember the tab

So just leaving the shared address https://ui.perfetto.dev/#!/?s=96c9XXXXX on the remote browser address bar sounds fixing all issues.

Start by reproducing the Share flow in the Perfetto web UI and compare the URL before and after opening the shared trace in another browser. Done means the remote browser keeps the original shared URL, so reloads remain populated, the trace can be reshared, and multiple tabs remain distinguishable.

Written by the indexing model from the issue text.