Okay looking at your logs, not that there is a lot to go through, but there still are a few things that comes to mind.
First of all you need to keep a better uptime on Riptide, Healing Stream Totem and Elemental Blast. I see Elemental Blast not even being cast, that is a lot of potential spirit/mana that you are losing out on. Just by pressing this spell once in a while, you will have massive mana gains. Riptide and Healing Stream Totem should just be used on cooldown, or as close to as possible, Riptide because you want as many rolling as possible to aid in maximizing Chain Heal jumps (paired with High Tide), Healing Stream Totem simply because it is insanely strong.
You can do something to help make it easier to use Elemental Blast, you can set the boss as focus before pull and make a focus macro for Elemental Blast, then you don’t have to actively target the boss when casting it:
#showtooltip Elemental Blast
/cast [@focus] Elemental Blast
With lower spirit levels spamming Chain Heal is simply not an option, you have to weave your spells with more thought. And this is where optimizing your small cooldowns come into place, because Riptide and Healing Stream are both cheap strong heals.
Looking at Socrethar I saw something, when the fight ended you were close to 100% mana. This is something that should almost never happen as a healer, you should always strive to be completely ‘dry’ when the boss dies. It is somewhat of a fine balance to find, but it will happen with experience. At least on that fight you could’ve been a lot more aggressive with Chain Heal, and it could potentially have done more for your healing. You should just try to make it a habit to evaluate each try, see if there are places where you can afford to pump out a bit more healing at the cost of mana.
You also only had a single cast of Spiritwalker’s Grace, in my opinion that is something that could be improved, from my experience at least there are more than a single situation where movement is required. You might just as well use it to get as much active time as possible. Could also mention Unleash Life here, this is a spell that you usually only want to cast when you have to move, otherwise it is a direct hps loss simply because it is so weak compared to all other options.
I just looked at your armory and saw that you were running with Glyph of Water Shield. There is really no need for this, it is rarely procced often enough to make up for the passive mana you lose by taking the glyph.
Can probably do a better job with more logs to go from 😀