How do I add Cygwin to the File Explorer's context menu in Windows?

Step 1

Install chere.

Step 2

Execute in Cygwin:

chere -i -s bash

It adds an item to the File Explorer's context menu:
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Step 3

I delete the HKEY_CLASSES_ROOT\Directory\shell\cygwin64_bash branch from Windows Registry because I never open a console by right-clicking on a folder icon: I always click on a folder window's background instead.

Step 4

Open the HKEY_CLASSES_ROOT\Directory\Background\shell\cygwin64_bash branch of Windows Registry.
Replace «&Bash Prompt Here» with «bash»:
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Now the Cygwin's menu item looks like this:
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Step 5

Now I will add an icon to the menu item (similar to cmd and PowerShell 7).
Add the «Icon» key with the «C:\tools\cygwin\bin\mintty.exe» value (actually, I do not use Mintty, i just use its icon):
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Step 6

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Step 7

Set up the appearance.