It would be extremely helpful if the Timeline view (especially in the mobile app) had the ability to filter on source, date & time. And/or perhaps a simple keyword search 
+1
But since it’s sort of unchanged in the last 6y, I use Simple log app cards for not urgent notifications, and CallMeBot Signal & Telegram when I want to see notifications (right away).
OK, these apps are cloud based, but these have the tools you (and I) like to see in notification logs.
In the web app timeline overview we can use the browser search function, but that’s pretty basic.
Simple log logs can be viewed per html page though, 100% local, also searchable with browser search:
