I had a look at the game through videos. I cant play it myself (so I just took screenshots from a video of it) as the arm positions needed to use some of the guns would just wreck my shoulders (like the shotgun/rifle) but I think I have an idea as to what you need to do.
SCREENSHOTS WOO!!!!!!!!
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Once you're done with all the shooting, it looks like you're meant to come in here and get a loadout ready. Note the box in the back. The game had actually pointed this out earlier, on one of those chalkboards, but it wasnt as brightly lit as the floating text boxes.
As for the grenade section specifically: It actually didnt look like there were any specific targets to hit. Just throw a couple to get used to them. But after the guy did all the target shooting with the normal guns, it was into here to do this part.
And then this happened:
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That door there, my good sir, will end this particular scene.
Generally when it comes to stuff like this, there are some good rules to follow, in order to figure out what to do next:
1. Read everything. If there isnt some magic floating text somewhere, a hint could be somewhere else... written on a wall or on a note nearby or something. Unless the situation you're in is very specifically meant to be a puzzle, most games like this WILL explain themselves somehow.
2. Touch everything. Sometimes it's just a matter of grabbing the right thing even if it's not lit up or even if you werent able to grab that thing earlier (as some objects may start out inactive, but become interactable once certain conditions are met.
3. Many games give you objectives, which you can usually view in some sort of pause menu or something. I'd bet this game has one, most shooters do.
Do try not to get frustrated, you can do it! Let me know if you're still confused!
Have fun with it, this definitely looks like something you'd enjoy. Though it does look like there are some slower parts from what I saw in the video.