The error code is saying that it is trying to do relative import and it cannot find the file _wsgi_encoding_dance in the _internal folder within the site-packages/werkzeug package.

Check the package requirements and make sure to install the correct package dependency versions.

gevent.wsgi was deprecated for years and was finally removed in gevent 1.3. There's an open bottle bug for this problem. Some of your options are:

1. Use a different WSGI server. You can directly use gevents wsgi server with python -m gevent.pywsgi my_module:my_app. Or try gunicorn
2. Downgrade to an older gevent
3. Patch the bottle sources to not have the broken import. gevent.wsgi simply did from gevent.pywsgi import *, so anywhere you see wsgi.Thing just replace it with pywsgi.Thing.

When this happens, it's an exception handler hiding details. If you import the root of your app from a Python shell (in a virtual environment, if that's what you're using), more will be revealed. Here, I forced an error in one my apps:

(venv) $ python
Python 3.6.9 (default, Jan 26 2021, 15:33:00) 
[GCC 8.4.0] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import wsgi
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/home/vagrant/toydeploy/wsgi.py", line 3, in <module>
    app = create_app()
  File "/home/vagrant/toydeploy/app/__init__.py", line 62, in create_app
    from app.errors import bp as errors_bp  # noqa
  File "/home/vagrant/toydeploy/app/errors/__init__.py", line 6, in <module>
    from app.errors import handlers  # noqa
  File "/home/vagrant/toydeploy/app/errors/handlers.py", line 6, in <module>
    oops
NameError: name 'oops' is not defined
>>> 

Installing and using flake8 is another way of spotting problems early.

After being prompted by abarnert I realized that it wasn't a problem in the larger structure of Flask and Apache but simply with the structure of my import. So my solution that got it working was to make sure first that I did

from web_tool import web_tool as application

Because my project structure looks like

/path/web_tool/src/web_tool/
    web_tool.py
    web_tool.wsgi

I think naming the folder the same as the main python script the same confused but then I got it straight. Now the above import still didn't work because I got a module error but what did work was:

from web_tool import web_tool
application = web_tool.app

I didn't see this structure anywhere else online or in any other SO answers but that is probably because of my particular project structure.

So with some help with my friends (IE: SysAdmins), we got this figured out last night. I learn best by example, so let's assume you're running Apache with mod_wsgi as Linux group apache with user flipperpa. Let's assume you're hosting in /home/my_project with wsgi.py in my_project/wsgi.py.

At the top level (ls -l /):

drwxr-xr-x.  47 root root  4096 Jul  9 09:43 home

In the home directory (ls -l /home):

drwxrwsr-x   7 flipper        apache 4096 Jul 29 10:22 my_project

This was the key. The lower case "s" means the apache group's setgid bit is set, and the execute bit is set. The final "x", of course, means anyone can execute.

Check your permissions down the tree; this did the trick for us.

After 2 horrible struggling days, I figured that the culprit was init.py that I accidentally put into my project's main folder and Heroku was treating it as a module. Removing init.py solved the problem.