How to operate an iPad from a Mac or Windows PC?
You cannot wake an iPad with standard software from the desktop. You'll have to use one of the iPad models that support Tap to Wake instead (i.e. they can be woken up by touching the screen, and/or for some models by using the Apple Pencil on the screen).

For demoing the webpage you can use the Safari Web Inspector. On the iOS device you'll need to access System Settings => Safari => Advanced and then enable "Web Inspector".

Connect the iPad to your iMac and open Safari on the iMac. From the desktop Safari's Preferences, you'll need to enable "Show Develop menu in menu bar" in the Advanced tab.

Now you'll have a Develop menu in Safari where iPad has its own submenu. When you open Safari on the iPad, you can choose it from that menu - and you have various tools at your fingertips. For example you can highlight elements on the page using the element finder, or you can navigate to other pages, run Javascript code, or whatever you would like.

The above works because your use case is specifically to demo a web site. There's no generic solution for remotely controlling the iPad across the wake screen, home screen, built-in apps, third party, apps, etc. Solutions exists that allow you to see the contents of the screen (for example using Quicktime to record on the iMac, or using third party solutions such as TeamViewer). However, none of those allow you to remotely control the iPad.

It is possible to integrate remote control in specific apps, but it requires you to be able to modify the app - so it is in practice only an option for the app developer.