I've tried doing the select armature in pose mode switch to object mode then weight paint thing but it still doesn't allow me to select bones among a plethora of other solutions and I'm not sure why but for some reason it just doesn't work for me. Can anyone help me figure out what I'm doing wrong? https://drive.google.com/file/d/1neePPk9PlKjhpp8AIbUOF94m1KHws7hX/view?usp=sharing
Edit > Lock Object Modes > uncheck
Then you can select multiple items when in edit mode. Set your mesh to weight paint while your rig is in pose mode.
Select armature - go in pose mod - shift + select mesh - go in weight paint - select bone with ctrl + left click.
Edit: video with your file