If I kept the separate drawer under the table I would have lost space, and needed a second set of drawer slides. Plus with the table pulled out I still could not access the items in the drawer!
Rather than a fixed drawer, which can’t be accessed when the table is out, as you pointed out, have the drawer be part of the table. Yes, you’ll need another pair of slides, but this way you can open and access everything in the drawer whether the table is stowed or pulled out. Moreover, cutting up the tabletop will make the table difficult to clean and particles will keep falling though to the drawer. Just something for you to consider.
Take a look at the installation video ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-D0s5GgO7ZmM.html "Van Life Pull out table installation - Heavy Duty Drawer Slides" That should help answer your question.