Wrote up a tutorial for getting the contents of your iPad's screen into OBS on macOS for streaming or recording or what have you. Connecting OBS to a streaming service is beyond the scope of this tutorial, there's already plenty of such tutorials around. I made this because it was a pain trying to find this information, as most info is either about 10 or more years out of date, or suggests using the native airplay features, which are nigh useless for this since that completely hijacks your Mac's screen, requiring you to try operating OBS blind.
Oh, and Windows and Linux are also out of scope for this. Though I've heard rumors that the (not free, though there is a free trial) AirServer app might provide a better airplay receiver option for both Windows and Mac. I don't know anything about Linux solutions.

Note that this will share your entire iPad screen, including notifications. You may want to set your iPad to "Do not disturb" mode while streaming.

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Anyway, here are all the steps above in proper text format, in case it's easier for anyone needing to translate or use a screen reader:

1. Plug your iPad into your Mac. I've tested with a Thunderbolt 3 cable. Lower quality USB cables might be work fine, but I haven't tested any.

2. Open Quicktime Player. Select File > New Movie Recording

3. A window will open. If it doesn't automatically select your iPad's screen, click the ⌄ next to the red dot record button and, under Screen, select the name of your iPad.
The Quicktime window should show your iPad's screen. You can now send Quicktime to the background, but don't minimize it, or it will pause.

4. Over in OBS, in the Sources panel, click the + to add a new source and select macOS Screen Capture

5. Give the new source a name and click OK

6. Set up the Method as Window Capture and the Window as [QuickTime Player] Movie Recording. Also recommend turning off Show cursor.
Note: OBS will remember this source, but if you restart Quicktime Player, you may need to redo the Window setting in this Properties window. Right click the source in OBS and select Properties to open this window again.