Maybe it's worth going thru this list a little for prosperity, since I've lived here for nine years and until BA's changes was nearly exclusive to oneworld. However, I only travel business at this distance - my wife's firm does sometimes enforce economy for internal meetings though (boo!)

• CX / Cathay Pacific: 5 flights a day to London, lots to the rest of Europe. Great service in economy, PE, business or First. Despite lots of flights this is the local "flag" carrier and as a result most people in Hong Kong collect Asia Miles, many want to go to Europe, and any of these flights is going to be stuffed full of both corporate travellers and Cathay status members. Your chance of a proactive upgrade beyond being Diamond ("top"ish tier) are fairly slim. And in advance lots of people are watching to get seats. Now, I have gotten business class single seats on miles before at short notice, but you won't be able to reimburse via work I presume. Then the other thing to be careful of is that the lowest priced ticket buckets (in either economy or PE) don't allow upgrades for cash or miles at all (and this is enforced). So, arguably the best airline and direct, but the lowest chance of an upgrade.
• BA / British Airways: Has gradually reduced to a single flight a day to London, that is quite a lot more expensive than the local flights, to the point where I presume they mainly want to fill it with ex-Europe passengers. Certainly for a year when they'd consolidated two flights into one it was leaving pretty much full, now I see some space. BA does offer proactive upgrades for cash, and will allow miles upgrades on travel-agent issued tickets as well (though I don't think, except for the 360 days in advance bookings, you are going to find many seats. So conceptually you have a reasonable chance of getting a paid upgrade. But BA PE is not that much better than economy, and if you had to fly their economy it wouldn't compare to the other airlines in the market. It is direct though.
• QR / Qatar Airways: Offers two flights a day out of Hong Kong (very rarely with QSuites sadly, mostly are old Cathay planes) with excellent onboard service. In economy you can pay a "seat fee" on the Cathay planes (about USD150) that gives you a cathay premium economy seat, but economy service (not so sure but perhaps free if you have status with OW). The Cathay planes (77W) are the ones to aim for if you are looking for an upgrade as they have more business class seats, the PE seating benefit I mentioned above, and even first class. In fact they fairly regularly have availablity in business and first class to redeeem - though much of it is QR "flexible" miles, i.e. double price. Apart from the transfer in Doha (which some many prefer), the overall experience is excellent - and the majority of your second leg will be in a full long-haul flight, particularly to London (think they cover at least 2 airports there, with perhaps 8 flights a day?). Just be careful as the cheapest tickets often book into a BA flight on LHR-DOH (With a QR codeshare), which isn't going to be great for either BA Avios earning or a good plane experience. Could be a useful route towards OWE status as well, as fairly easy in this case to get your 4 QR segments needed for status
• JL / Japan Airlines: Got to be one of the world's best premium and economy cabins out there with excellent Japanese service, good quality cabins/hardware, though your movie selection may be a bit worse than other airlines here (i.e. fewer movies and older, as they tend to have both a Japanese + International version). The lounges in Haneda or Narita are excellent, their staff try their best to look after you, and the other people on the plane are more likely than not to be considerate Japanese people. It is going to be pretty expensive, and you are competing with a bunch of Japanese and HKers who also have plenty of JAL miles that they are trying to use up. I can't imagine your chance of an upgrade outside of the JAL programme are high, nor do I think they offer cash upgrades really. But it would be a great flight if your employer has a view that "any economy ticket is ok, no matter the price". Their PE is also not too dissimilar (in my own view) from BA's 2-4-2 ying/yang business, worse seat, but better service and food. Note, due to Russian airspace closures now often routes to Europe over the North pole / America, so you do go the long way around.
• AY / Finnair: Historically offered great flight deals (particularly in business class) and their concept of "the short way to Asia" really did work nicely - transiting via Helsinki, often in under an hour, was smooth and whilst it isn't for everyone their business class "couch" seat does seem to work. My main complaint is that now its the long way to Europe - you spend 15 hours circling the world to get to Helsinki - then head back to Europe - typically on short haul planes (that in the case of regional airports are often very small / not great seats). You can get one or two long-haul flights a day to London, A350s, which are the ones to aim for. I generally think of them as 'discount business class' but it can be reasonable value in a sale. I'm a lot less certain on their premium/economy experience, but in my mind it sits below any of the other airlines here except BA in terms of service/food. Believe you'd be happy with entertainment. Oh and most of the time no PE after Helsinki (except on the flights above), so hours of your trip will be in economy anyway
• MH / Malaysian Airlines: I used to travel them all the time pre-COVID around Asia as they had a long-haul plane to HKG and lots of sales. Since COVID they have been re-building, but my main issue with them now is that you will get (at least for the next few years) a short-haul 737 between HKG and Kuala Lumpur, which does have some entertainment but it's a pretty cramped experience (admittedly in business it is marginally better, but you just get too used to lie-flat beds inside of Asia). Once at KL I think you'll get a nice new A350 plane to London (their only European destination outside of Paris). You've got Asian service, a reasonable entertainment selection and food that I would consider is pretty reasonable. It's not as good as CX/JL or QR, but above the two European airlines. Transiting at KUL should be fairly simple, the lounge is ok if you have access, my only final lingering concern is that they weren't always great at timeliness of planes or cancellations as they have a small fleet, so if there is a problem they need to fix the aircraft long-haul. I don't really have a view on upgrade liklihood, though some people as pointed out above, have moved to Enrich to replace BA as their FFP. They do offer paid upgrades for cash via MHupgrade - which is fairly expensive due to being an auction - but that could work out well if you don't mind that your employer is paying half your ticket prices and you pay the other half to business.

If considering non-oneworld, which isn't always a bad idea if you don't have status to get into the Cathay lounges (which are great and make oneworld so much better than any other alliance in HK):

• I have also recently started to fly occasionally on Emirates/EK, a good economy product, excellent entertainment, and they are about to start sending their new planes with premium economy to Hong Kong too. Their upgrades are very expensive though for miles (unless you earn lots via CC spending or hotel stays), but it is a reasonable option. My preferred is pay for business/get first with miles, which is nice on the A380 with a shower and caviar/krug.
• You can fly any of the Chinese airlines very cheaply via some Chinese city - often Beijing or Shanghai, to Europe. I would look at them purely on price as otherwise they've got reasonable hard products, but service can be a bit hit or miss from perception.
• KLM/Air France/Lufthansa/Swiss: Marginally better than BA, will be cheaper, but then you end up with a short haul hop in a pretty rubbish European set-up. I presume hard to find seats for miles as HKG is a premium destination still
• Korean Airways / Singapore Airlines - two other great airlines with good service, similar to JAL above - i.e. more expensive, but excellent service, hardware and treatment. But will be a longer way to get home as like JAL you're heading the wrong way first. Also going to be hard to find upgrades for cash or miles.

Happy travels '