Don't go and just randomly disable Search or Cortana completely - that usually doesn't help and can break other things. The annoying part is that Windows 11 can really be sluggish with this, even when your hardware is actually fine.
What I'd recommend: take a look at your startup programs. A lot of apps hide themselves there and load in the background, even if you don't actually need them. Go into Settings, search for "Startup" and disable everything there that you don't really need. Often it's sync tools, cloud services or stuff like that blocking the start menu. That's usually a faster solution than all those indexing tricks.
If that doesn't help, try this: open Task Manager (Ctrl+Shift+Esc), go to the "Startup" tab and check how much CPU and memory is loading there when you open the start menu. If something goes haywire, you've found your culprit. Sometimes it's just a Windows Update indexing something - then just waiting and restarting helps.