Bump. Got the same bug. Literally game breaking when you can't participate in combat in any way. Ppl suggest going to 3rd person and back to 1st person to fixes it, but not for me, nor many others. Some suggest it might be because of a "stuck conversation" with some NPC and to fix it you'd have to find this NPC and have a chat with him / her again. I have scoured through the wasteland, chatting with every NPC I could think of and have yet to fix the bug.
My bug occurred after finishing the Reunions quest and trying to talk to Nick straight after exiting the building and seeing the BoS airship. When Nick refused to chat with me, I figured I'd fast travel back to Diamond City and talk to him at his office. I found him there (along with Piper), talked to him and finished the quest. After picking up the follow up quest, the bug appeared and I was unable to draw out my weapons, or use V.A.T.S.
Only option for me would be to reload a save 7 hours of gameplay prior to this bug, when my guns still worked. Rip motivation.
Here is a video recorded by another user showcasing the bug: https://www.youtube.com/watch?v=ylzpeb5EjUs