Using HomeBrew on OS X

I am looking to improve my use of HomeBrew package & application manager 
[https://brew.sh/] on OS X - having installed Ventura on a 2012 macpro 
unibody (thank you Open Core Legacy Patcher (OCLP).

In the past, I would search the CLI or happen to know/find out that an 
application I use was on Brew.

I tried installing some Brew GUI tools this evening, but none were that 
great (TBH). I could search for packages or casks, but ones I knew are 
out there were not listed in the results - very frustrating.

How do folks find things in the Brew ecosystem,  Is there an easier way 
to find applications within the Brew ecosystem?

Is there a way to script or automate my normal application installs with 
Brew?

TIA!