The ADB method is easy enough, but I may not have a computer at hand. Can I retrieve the PID with a Termux package or an app, or any other methods (including those which require root)?
If you are using Android 7 or above, you need to have access to ADB (either command-line client, or an app which used adb on localhost) or root access to see the PIDs of other processes.
If you are in Terminal emulator app or in Termux app, and you have root access, do this:
su ps -A -o PID,USER,NAME
This would output text segregated in three columns: first column as PID, second column is the user which owns the process, and the third column showing the name of the process.
Example output (posting only a snippet of it here):
28574 system net.oneplus.odm 28622 u11_a149 com.oneplus.gallery 28646 u0_a149 com.oneplus.gallery 28701 u11_a149 com.oneplus.gallery:recyclebin 28727 u11_a149 com.oneplus.gallery:contentdetector 28778 root [kworker/1:2H] 28789 u0_a329 su 28794 root sh 28872 u11_system com.oneplus.opbackup
ps command, can also use
pidof as suggested by Yahya Uddin here.
Note: PID and UID are altogether different things. If you are after UID, see How can I find app name by UID?