9700k memory speed limitations

[Biscuit Boy]

So I'm trying to round out my system through upgrades right now, and since graphics cards from this gen are nonexistent on shelves or sites, I'm thinking a memory upgrade would be small and easy. I have 2400mhz ram in it now because that's what I could get my hands on like a year or two ago, but since I went and got a 9700k for my z390 board I'm thinking that it might need higher speeds to do a bit better overall. I remember hearing about Intel locking mem speeds on some chips at some point in the last 6 months or so, but I don't exactly remember which they were, what gen, or otherwise. My questions: 1, is the 9700k's max memory speed locked at 3000 mhz or below, or is it fine to go with higher speed? 2, if I can go higher speed, should I buy 3200 mhz or aim for 3600 mhz ram, and has either gotten cheap enough to go 32gb instead of 16gb? Finally, is it even worth upgrading my ram at all on this processor? I feel like it's fine where it is with xmp and a mild clockspeed oc but I don't know if higher speed ram even benefits me at all for it to be worth it. Thx for the help and advice in advance.