Click-lock Alternative?

There is a built-in equivalent for trackpads, called dragging, which you find in System Preferences > Accessibility > Trackpad Options:

In case this is not sufficient for you or you need to use a mouse, have a look at the answers to this question. Currently the following third-party apps are being mentioned:

• Hammerspoon (free) is a popular choice for gestures and automation. It offers a feature called "Grab Scroll".
• Karabiner (free) a similar and popular tool.
• Smooze (commercial)
• Smart Scroll (commercial)

Better Touch Tool (commercial) is my personal favourite as it allows so much more, such as another Windows-inspired feature, called window snapping, etc. The procedure here would be as follows:

1. Open BTT preferences
2. Select Input device, i.e. Mouse
3. Select Trigger. The one you mention (i.e. long press) currently seems not to be available. (I suggest you make a feature request on their forum. The developer is usually very open to such requests.) Instead you could do e.g. middle-click.
4. Select action. Go to Window Resize & Move > Start/Stop Moving or search.

This is an incomplete solution because it doesn't answer the question as asked.

I'm hoping someone can find a solution that may involve the trackpad/gestures control panel, but I don't have any machine with one so I can't test.

In the meantime, if you have an extended keyboard, then Mouse Keys might go some way towards, if not exactly as asked, then some way towards achieving a similar result.

In System Prefs > Accessibility > Mouse & Trackpad there is Mouse Keys [in the Options you can set it to toggle on/off by tapping Opt 5 times]
It enables the 10-key NumPad on an extended keyboard to be used to drive the mouse cursor. 123, 46, 789 act as directional navigators. 5 is the click. I had hoped that with Mouse Keys on, it would allow you to press 5 & then drag the actual mouse to carry out the task. Unfortunately it won't do that, they seem to partially ignore each other. Any 'real' mouse seems to act independently, so 5 will click but dragging the mouse won't 'carry' that click.

However, holding 5 & using the direction keys, the click does 'hold', so click & hold a title bar, for instance, then the keys will 'carry' the window until you release 5.