So to summarize everything that was said and what I've found, for future noob comers here as I am, here is the answer I find the fullest:
Var. A. For very simple situation the easiest built-in tool is just use
Select -> Select all by trait -> Interior faces
And then delete those faces.
Unfortunately, that does not solve the situation for anything else than a very simple geometry case.
Var. B. For many cases there is another way, that is also very simple. Thanks to james_t for pointing to this method. I think it is the best middle ground here:
First in edit mode select all with A
Check that options Auto Merge and Split Edges are both active and you have a least some understanding how they work so you've set the right Threshold depending on your object's mesh and its dimensions.
Now press G and move it all a bit so that auto-merge kicks in. The best way to keep the object in place is the following sequence: G, Right, Left, Enter
But you can do this even by mouse if placement is not of any importance to you.
Now you've prepared the mesh for next step the best way you could.
Press the / to isolate the object for everything else.
Disable the option "Toggle X-ray" if active.
Deselect everything ALT + A.
Now select all the external faces by any tool you find best. I prefer "Select box" tool. Just few Shift + LMB + rotating.
And finally, invert selection Select -> Invert or CTRL+I. You should have all the internals selected. Delete all the selected faces.
This should do the trick, but you may be left with some faces that are still partly inside, because the Auto-merge option, unfortunately, is not perfect. Though you can fix this by merging few vertices manually, if not many.
While it is a long explanation, it is a very simple method. Just wanted to make it clear to newcomers.
Var. C. If you have a very complex mesh and the above-mentioned simple solutions do not suit you, you are left only with more complex non-integrated solutions. And here you should definitely check the idea by Rick T with geometry nodes.
While it is a complex thing to do yourself on a noob level, Rick T has done all the job for you.
So, you only need to import object from blend file to yours and copy modifiers CTRL + L from his object to yours.
You can edit the nodes in Geometry nodes editor, to suite your case.
Afterwards, apply the modifier and delete everything that you do not need anymore.
Read his answer for more info.
PS: I think that there should be a simple integrated solution for such clean-ups in blender. Especially, considering that it is so popular now for 3D printers, and all that nonmanifold internal faces are a huge pain for this job. And I hope it will be added in future.
PPS: There may be other solutions, and some for more limited situations. Check answer by james_t for example.