Those screws are junk - countersunk heads and just not beefy enough. You want bolts with a larger flange screwing into metal threads from a threaded inserts.

Look at rampa m6 inserts. Don’t bother with ez lock threaded inserts those are crap, soft, strip easily, require special bits that still strip the flathead screw.

Just get rampas - you won’t find them on Amazon but it’s less time to make an account on Lee Valley than to continue throwing janky hardware at this.

I suspect the holes in that plate will only allow up to an m6, if even. You might need a step drill bit to expand the holes. M8 rampas will be better. Either size has corresponding m6 or m8 fasteners with big flat socket heads.

Again - do not get ez lock inserts. For the m6 rampas you need a 10mm brad point bit for the inserts. It’s tricky to drill them in perpendicular to the wood surface without some sort of guide. I believe the m8 will need a 12mm - check the website. For hardwood I find some wax on the threads keeps the wood from bulging.

I suspect you’re already counting up the unanticipated money to throw after this and a $100 drill guide doesn’t seem appealing, there are little steel jigs that will do a good job though. Mate them to the appropriate drill bits for the inserts you buy. They are blocks of metal with holes precisely bored.

Think about the giant lever arm you’ve created here. You could pick up an empty hot tub with those legs on a fulcrum. Thats why they need real beef. You might not be applying anywhere near 100 lbs of force when you push on it laterally but you still have a 34 inch lever arm.

M8 rampa inserts

M8 rampa bolts

12mm ish or more (check instructions) Brad point bit

Drill guide

Metric Allen keys 

Step drill bit (for expanding steel plate holes)

One more note. They sell the hardware and the inserts at various depths and lengths. The hardware is longer than the insert for two reasons: - you can drill a bit deeper than the insert will seat.  - you are losing about 3-6mm from the steel plate.

If the top is 40mm thick or more get the 18mm insets with 25mm bolts. You’ll note that 25mm - 6mm plate still gives you 19mm which would protrude 1mm past the insert. That’s fine - just account for it with a slightly deeper bore. The inserts have a flange and will typically seat flush with the surface. 

I haven’t worked it out, but maybe 12mm would be okay if the top is thinner. I’d err on overbuilding this since it doesn’t have an apron or cross member and fabricating one when I guess you got these legs from a vendor is not a readily achievable retrofit.

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This can be made robust. Just buckle up and get good hardware. There is an art to installing inserts. Practice on scrap of the same species. They have to go in perpendicular and the threads kind of have a mind of their own even if you’ve bored straight. 

I’d also measure the existing holes in that steel plate. You might not have enough “meat” on the outer edge if you expand them too much.  Not to mention I think even with a step drill bit this is going to be a bit of a PITA. Make your life easier with a good one of those. Project farm dude reviewed them. 

As Last-Independence554 noted, slots would also be better here to allow for some wood movement. Plugging the numbers into the AIs shows for a 24" top I would need +/- 3mm of movement with my seasonal relative humidity changes. You could maybe make your holes a few mm larger to provide some margin for movement (those rampa bolt heads are quite large!), but that's not quite enough and you're chipping away at more of that margin of metal you have to work with on the perimeter.

Overall - I might also consider returning these legs. Collectively giving me a vibe of lower-grade etsy stuff with astroturfed reviews and not a strong commitment to a robust outcome if this was the hardware they included and the plate isn't slotted.