As sketched I think cam connectors would work here, as long as the centre of the table isn't subject to excessive weight in use. But I think there's an easier way of doing what you want, and it would allow the insert to be placed and removed far more quickly.
You can achieve the same result more easily by just having the insert sit on a 'shelf' all round. This shelf can be a rebate formed in the frame or you can use built-up construction and tack on strips underneath which many would find simpler to do. This also means the frame members can be thinner wood, for a possible significant saving in materials cost. The strips don't have to be the full length of each side, so you wouldn't have to mitre their corners or worry about getting them to exact length for a neat fit.
Advice on recommended joinery for the frame corners is also welcome!
You could go with the simplest option which is basic mitres and just reinforce the glued joint. Mitres that are glued only are quite weak (although that can be improved on by good glueing technique) but they can be reinforced by various simple means, e.g. using nails, screws, dowels, or corrugated fasteners AKA wiggle nails.
This method keeps the basic joint very simple and straightforward to cut while ending up strong enough to last in use. My personal favourite here for reinforcement would be through-dowels as I like how the exposed dowel ends look, but the joint may actually end up being stronger than if screws were used similarly since they are going into end grain*.
Can't ignore wood movement
Regardless of the details of the built do bear in mind my previous Comment about movement in solid wood. Even if you carefully select quarter-sawn material to make the panel you're likely (i.e. in most species) to get enough expansion and contraction through the seasons in a panel 20-24" wide for it to be an issue, unless the climate is unusually stable where you are.
This isn't just that you'd have a sloppy fit sometimes and a tight fit others. If the panel is sized to fit well initially and it subsequently expands by only a fat 1/32" / ~1mm (which is a conservative assumption) that would be enough to prevent it being placed, or if in position to jam so tightly it couldn't be removed.
But if you make the insert from plywood or another manmade board you avoid this issue entirely. This is actually the only stable way to make any sort of picture-framed table (inless the effect is achieved by veneering).
*See Endgrain screw withdrawal force for a bit on this.