There is no search currently for AudioSuite. How many plugins you have depends on the exact plugins you own. I personally have a ton of AudioSuite plugins and a search would be helpful.
But, you can set Pro Tools to display Category and Manufacturer for plugins and this carries over to AudioSuite as well.
So, if I know I need RX Voice De-Noise, I go right for the iZotope folder, for example.
https://benonistudio.com/find-your-p...-in-pro-tools/