In Windows PC, when some computer is very slow, I use software like SysInternals Process Explorer to check background programs that is using more CPU/RAM. I use SysInternals AutoRuns to disable auto start programs too.
In android device, what tools/procedures can I use to diagnose this kind of problem?
I don't think you'll be able to control start-ups but you can surely monitor CPU usage. Open Settings>Developer options - and under Monitoring section enable Show CPU usage. CPU usage and processes will be shown as overlay on screen. Also there are number of apps in Play Store to serve the purpose.
You can go to Settings -> Developer Options -> Running Services to see the active services that are running. From there, you can click on "Show cached processes" to check the apps that may be not running but are cached by the OS in case you need to run them so they can be started quickly. You can then stop running process or cached processed.
In Lineage, Settings -> Privacy, you have options to disable permissions given to apps. You can even disable apps that start at boot.
