Mistweavers gain the most from using Soothing Mist to get extra instant casts of [Vivify] and [Enveloping Mist]. If the intention is to cast multiples of those spells on the same target, then the instant cast potential of channelling Soothing Mist may actually save time over regularly casting the spells. Additionally, Soothing Mist continues to provide its extra channeled healing as Vivify or Enveloping Mist are being instant cast. [Clouded Focus] is a relevant talent for using these combinations.
During Legion, when Soothing Mist was a passive spell that triggered after many of the monk's other healing spells, it could be channeled for up to 600 ticks. With 0 haste, Soothing Mist healed every 0.5 seconds, meaning that the channel would last a total of 5 minutes.
Patch 10.0.0 (2022-10-25): Now a row 1 class talent (was a level 17 Mistweaver ability).
Patch 9.1.0 (2021-06-29): Channel is no longer interrupted by Mana Tea or Zen Focus Tea.
Patch 9.0.1 (2020-10-13): Now learned at level 17 (was 10).
Patch 8.1.0 (2018-12-11): Soothing Mist is no longer dispellable.
Patch 8.0.1 (2018-07-17): Changed back into an active ability. Heals the target for (320% of Spell power) over 8 sec. While channeling, Enveloping Mist, Surging Mist, and Vivify may be cast instantly on the target.
Previous: Effuse, Enveloping Mist, Vivify, Life Cocoon, and Sheilun's Gift also trigger Soothing Mist. After casting these spells, you continue to channel healing mists into the target, healing them for (64% of spell power) every 0.5 sec, until you take any other action.
Now heals for 64% of spell power per tick (was 55%).
Hotfix (2016-10-13):Soothing Mist healing reduced by 10% in PvP. (Soothing Mist version of Ancient Mistweaver Arts is unaffected.)
Hotfix (2016-09-28):Soothing Mist is no longer interrupted by Spirit Tether.
Hotfix (2016-09-15):Soothing Mist cast from the Monk's Jade Serpent Statue should cancel on targets farther than 60 yards from the statue.
Hotfix (2016-08-02):Soothing Mist should no longer fail to cast when repeatedly applied.
Patch 7.0.3 (2016-07-19): Redesigned into a passive ability. After casting Effuse, Enveloping Mist, Vivify, or Life Cocoon, you continue to channel healing mists into the target, healing them for (55% of Spell power) every 0.5 sec, until you take any other action.
Previous: Heals the target for (918% of spell power) over 8 sec. While channeling, Surging Mist and Enveloping Mist are instant, and will heal the soothed target.
Soothing Mist's healing has been increased by 100%, its GCD has been reduced to 0.5 seconds, but no longer heals immediately, and no longer generates Chi.
[Soothing Mists].
[Accumulating Mist], 
[Calming Coalescence], 
[Clouded Focus], 
[Peaceful Mending], 
[Unison]
[Summon Jade Serpent Statue] provides extra healing while casting this ability.
[Vivify] and 
[Enveloping Mist]. If the intention is to cast multiples of those spells on the same target, then the instant cast potential of channelling Soothing Mist may actually save time over regularly casting the spells. Additionally, Soothing Mist continues to provide its extra channeled healing as Vivify or Enveloping Mist are being instant cast. 
Patch 10.0.0 (2022-10-25): Now a row 1 class talent (was a level 17 Mistweaver ability). 
Patch 9.1.0 (2021-06-29): Channel is no longer interrupted by Mana Tea or Zen Focus Tea. 
Patch 8.1.0 (2018-12-11): Soothing Mist is no longer dispellable. 
Hotfix (2017-03-07): Casting Enveloping Mist while channeling Soothing Mist no longer consumes Thunder Focus Tea. 
[Sheilun's Gift] now activates Soothing Mist.
Patch 6.0.2 (2014-10-14):
[Stance of the Wise Serpent]. 
Patch 5.2.0 (2013-03-05): Now generates chi more consistently and average generation rate is slightly higher. 
