Monk situation on Covenants is bit spec dependent atm.
For WW Kyrian and Fae are pretty trashy in terms of output. They are mainly about offering more resources (Chi, Energy) which is exactly what WW does not need. WW needs way to spend Chi, not gain it. As icing on the cake, the Kyrain one buffs your mastery (which rests upon you not spamming the same ability twice) whilst also flooding you with Chi which means to get rid of it you either need to spam the same ability twice, or use suboptimal abilities (like an aoe ability in a ST situation) to offload the chi and save mastery.
Venthyr is okay for output for WW, but it’s pretty boring and not very interactive. The adds cast fists of fury, so basically it’s a “summon pets that deal damage” cd. Easily best for ST, probably best for small target as well, but where more and more adds, join, i’d argue bonedust probably gets a bigger advantage depending on how dumb the pet ai is.
Necro can be decent in cleave/aoe situations but again, it’s not very exciting. It essentially just makes your abilities have a chance to hit harder, and makes your primary spammable aoe cheaper (but spamming violates mastery…so we have this problem again) but it will pull numbers in higher target situations, potentially more than ven
So for Ww it looks like Venthyr (ST) Necro (AOE) with Fae and Kyrian being niche picks where the gains they could have (the Kyrian mastery buff is pretty big) create too many issues in capitalising on that gain smoothly, whereas Venthyr just gives you free numbers, no questions asked.
Regarding BRM. Kyrian is actually pretty good as mastery can be useful, the reset on keg is alright and the extra damage taken makes it a good aoe dps cooldown
Venthyr is a bit meh, the monk adds cast breath of fire. If they interfere with targetting this may be a no go. I’d say Kyrian is a more reliable source of damage and has defensive benefits.
Necro has same damage benefits as WW, but it makes your energy spenders refund your brews quicker too. I’d say this one offers potentially less damage than kyrian, by more defensively by allowing you to quickly chain a couple of Celestial Brews. Would probably work nicely in a Blackout Combo build.
Night Fae is a another source of AOE damage and the additional effect is it casts breath of fire on damaged targets. The uptime for BoF is already quite high, so I wouldn’t say this is super essential. BrM do have lots of abilities that hit many targets however, so chaining the Faeline should realistically be quite easy. Primarily an offensive cooldown (probably one of the better ones) but the defensive benefits aren’t amazing.
I’d say the better ones for Brewmaster stand as Kyrian/Necro, followed by Night Fae, then Venthyr
Mistweaver kyrian gets a free essence font on their use, and it heals more at start and finish. at 2 mins this is a pretty big cooldown what is essentially a “refresh essence font” cooldown, although the power of the bonus heals may make it worth it. The thing about it is Mastery is generally good for Monks in dungeons (which this ability buffs) but Essence Font is your raid spamming ability, so the two components of this ability don’t match up perfectly. Raiding Monks prio crit over mastery given it buffs essence font in addition to buffing gust of mists healing (by allowing it to crit)
Venthyr shadow monks heal with enveloping mists. This could be a nice additional throughput cooldown in situations where the group will need some stable recovery. As EM causes all of your other heals to heal for 30-40% more, this almost behaves as a raw healing buff given the adds will semi-reliably spread EM around for you. Could be decent in raids but i think dungeon more.
Bonedust brew makes gusts of mists heal for more on affected targets. This will be a nice small (1 min) cd which is pretty nice for dungeons I figure to give your general ST and AOE a bit of a pop, but will not save anyone from death instantly, which Kyrian could situation depending.
Faeline Stomp causes you to heal nearby allies with one bolt from Essence font when you stomp. This will be nice for Fistweaver builds as it will build some gentle aoe healing in your dps rotation and give you some decent aoe damage.
MW is probably most balanced imo. Each one has some use somewhere, and the main difference between them is whether you fistweave or not, and whether you value having a party triage button, an easy to use “healing boost” which is location bound, or a potentially higher healing boost overall but requires you to smart target for the duration.
Faeline is good for fistweavers (in whatever content they’re in).
Kyrian is triage cooldown for aoe, giving instant aoe healing and then buffing mastery for vivify. Could see use in raids or dungeons
Venthyr will give you “free” healing without you having to do anything, so decent for PvP situations or situations where you may have to move around a bit or can’t afford to cast. The free healing will be weaker without you working “with it” to capitalise on the EM 30-40% buff however so I think this cooldown could be very good in hands of a skilled MW as it will allow you to benefit from EM without wasting time on casting it if you prio the targets and check who your disciples are targetting. Kyrian is more intuitive to use however, as is Bonedust. They will “heal more” if you “do less”, but Ven will probably heal more if you “do more” in a multi target situation at least. I think Bonedust will still beat it ST.
Necrolord is better for easy ST healing than the other three due to the flat mastery boost, plus the trigger chance on the proc being flat and Monks generate a lot of “ticks” on focus targets a second, meaning you’ll get a lot of mileage on this trait. It has some aoe applications due to the base effect, and the mastery buff doubling with with font’s “double proc” effect. It is location bound however, which is a limitation. I’d say this will probably be better than Kyrian for “general” throughput in similar situations, but it is not a triage cooldown, you have to anticipate in advance when you’ll need it, whereas Kyrian offers you an instant “heal the party!” button. In situations where you don’t want to play with disciples and tracking them, this will be better.
Thus ends my monk speculations.