Ctrl-Tab Improvement
Currently ctrl-tab doesn't know about which tabs have search results. It should change a little bit:

• If used while the text field is in focus, keep that focus.
• Only cycle through tabs with results.

Fuzzy Search
D9145 Needs to be altered to not use per-word comparison, instead compare the entire text block at once.

Performance
It's not yet known if search will be a bottleneck for anyone on lower end hardware. At least some efforts should be made to identify any performance issues, and possibly address them. I did some initial profiling. Although I didn't find any major bottleneck, it's possible some things could be looked at.

I tested by maximizing the property editor in a relatively complex file and ctrl-scrolling up and down very quickly, so it should be redrawing as quickly as it can.

Here are some interesting items from the "Bottom up" results:

• __strcmp_avx2: 5.52%
  • buttons_context: 1.15%
• UI_panel_begin: 0.85%
• BLI_strcasestr: 0.617% -- called from property search only
• panel_add_check: 0.61%
• uiItemFullR: 0.582%

I think the first thing I would consider is using GHash for buttons_context.c, similar to the recent changes in screen_context.