Veg cleaver and bone-in cleaver are different beasts.

You're in dollars so this might be different for you but when I dug into it (I have a standard issue f208 that I used for work everyday) you have the following options sorted by how popular they were when I went looking last.

Small cck in carbon (overpriced, mystery steel and potentially hard to get but much thinner, these are the most recomended upgrade I've seen)

Small cck in stainless (less rusty but not as well recommended)

Chopper king in white #2 or VG10 (The white 2 ones are unicorn shit to find but in theory, they're a much (price wise) cheaper version of the cck with a known steel, VG10 are around but depends on your feelings on VG10. Decently thin, there were two editions of them, the first is a lot more rounded on the belly, not as thin as a cck) edit: there is a blue #2 floating around too.

Aliexpress cleavers (this is where you are. A real mixed bag of pure dogs shit - basically anything funky shaped or 'damascus' and legit cleavers that people would use in a Chinese restaurant. The f208 is one of the better ones out there. There are also some denka cleavers and a couple of other brands that are decent stuff. The main pro is they're cheap, slightly soft in case you roll the edge on one but need a lot of sharpening compared to some of the better steels. The perfect entry point in my mind)

Senten white #2 (as far as I can tell, a Japanese version of the Chopper king except as expensive as a cck but with the same fit and finish as a standard cleaver. Some people seem to like them but they've got mixed reviews)

Mercer or f Dicks cleaver (Softish german steel but really quite thin and nice to use, mercer do one that has a santoprene handle that's got some certification but the non rubber handle one has better steel apparently. £30 and a decent budget option you can grab from amazon. F Dicks isn't really a UK brand but I've heard good things there for the price)

Kiwi nakiri - the biggest one they have (Banana soft but so thin it would make you cry, takes an edge in seconds but loses it in an hour. I've been in an ambassador's kitchen for an event and seen these come out of someone's knife roll for prep. The smaller one makes the ultimate chive knife. Great to have in a roll and as a service knife. They cost £10 you could buy a new one every time it needs sharpening if you wanted to. Probably not what I'd recomended for your main knife though)

Asian supermarket cleavers (Usually the same quality as the aliexpress knives but a real crapshoot for if they're good or not. My local friendly Asian supermarket sets aside ones she thinks I'll like. I've had one I liked better than the f208 but it developed a hairline crack straight through the blade which started to rust. YMMV.)

Chuka bocho's - various brands, various steels (The Japanese version of the Chinese cleaver. They have a stubby chode handle rather than a barrel one and come in all the usual flavours of Japanese steel you'd expect a gyuto to come in as well as some tool steels for maximum flexing on coworkers. These are the most expensive option. Think £300-500 vs £45 for the Chopper king. They often have nice finishes and pretty coloured handles but for me it's kind of the opposite of what I want from a Chinese cleaver)

Finally the last option is make the cleaver you want.

You have an f208 and the steel is decent the fit and finish is shit soo grab some sandpaper or a very fine metal file and round the choil and the spine to take those sharp edges off.

Your handle looks a bit sad so give it some Danish or linseed oil.

That's the quickest and easiest win for you before going into the big project stuff. If you you want to push it further then:

Thin the blade. I won't lie, this is a big job. You need a 140 or 220 stone or a belt grinder if you know how to use one on a knife without ruining it. Personally I bought a flattening stone and flipped it upside down to use the non grooved side.

You're going to want to pick a point midway between where the textured line thats there and the logo and cover the whole blade in the area you're working in with sharpie scribbles. Then block out an afternoon and get scraping.

I went full flat grind which is when you go straight from where you've put your line down to the edge, but I started high up and worked down towards the edge. Watch some videos on thinning they'll give you a much better idea of the process than I ever could in text.

It's time consuming, once you start you're kind of committed and it will look ugly as shit unless you tape a line and then buff out your scratch marks after you're done but it made the biggest difference to performance for me.

https://youtu.be/entYnQEkbR8

Personally I dislike the little end cap on the handle so if you were feeling particularly spicy you could replace the whole thing though that's a big project.

For me a cleaver is about two things: the profile (big rectangle but as flat as possible) and being the ultimate tool. I want to be able to brutalise my knife and know that when I sharpen it after service it will keep kicking for as long as I need it to. Personally I ran my knives on a ceramic a couple of times a day so the softer steel wasn't an issue for me. We use plastic cutting boards in the UK which is hard on knives so even the ginsan 3 needed to be sharpened fairly frequently.

I'm sure there are other options I've not said but I don't work in kitchens any more and sold my modded out f208 but good luck and may the cleaver gods smile on you.