Description of the new feature/enhancement

[Original Issue: #605] [Original Spec: #3299] [Initial PR: #3590]

Terminal text search has already realizes single tab case sensitive/insensitive forward/backward search. In phase 2, we are considering these new features:

[x] Add "Find" button in dropdown menu to trigger search. Now the search dialog is launched by key bindings, we may need to consider binding the dialog to a button in dropdown menu for mouse only operations.
- sorta in #13055. Close enough.
[ ] Search from all tabs. In phase one search are limited within one Terminal window. However, the community also requests search from all tabs. This may require a big change to the search algorithm.
- [x] Depends on #997 by all accounts
[ ] Search history. Sometimes users would do the same search for several times, thus, storing the search history is useful.
[x] High-light while you type. Emphasizing all the matches in the buffer with an outline or selection with another color. This provides a clearer view of the searched text.
- [x] #7561 Feature Request: Highlight all finding
[ ] Add size handle. Some text editors let the user resize the search box, and there is a size handle on the left side of the search box. This helps user when they search for long text.
[ ] #5314 Fuzzy Search
[x] #6319 No results notification (or reveal number of results)
- in #14045
[x] #7695 next/previous search key bindings
[x] #8307 Selected text should populate search box
[x] #8274 Add capability to insert matched hit
[x] #1527 Display "find" matches in the scrollbar, #8631
- in #14045
[x] Pressing next/previous match keybindings should move to the next needle, even if the dialog is closed. (Maybe it should auto display the dialog)
- Mentioned in #8522 and #8588
[x] It'd be cool if there was a shadow underneath the search dialog, like there is for the command palette.
- Mentioned in https://github.com/microsoft/terminal/pull/11105#issuecomment-911929402
- Fixed in #12913
[ ] Regular expression (regex) match. This is a useful search pattern and is implemented in some editors.
- first proto in #9228
- Will be effortless after #15858 merges
[ ] #4407

Also related, from #5001:

[ ] Add a setting to configure the regex used to detect patterns

[ ] Allow "hyperlink" matching for arbitrary patterns and adding custom handlers #8849

Theoretically, this could supersede #7562

Should be self-consistent with #8294

[ ] Control the styling of hyperlinks - attributes used for autodetected hyperlinks, and then different attributes for hovered ones #8294