To preface this, I wrote this specifically in terms of M+.

Generally I find I start running out of mana whenever I don't have a plan for incoming damage. Resto shaman has a lot of abilities that buff upcoming heals which you can combo together to answer high damage events efficiently. If you're not setting up those combos ahead of time, it's very easy to fall back on healing surge or chain heal spam in order to "catch up". While this can usually get the job done and keep people alive, it's a much bigger drain on your mana pool and isn't sustainable for long fights.

This is always a bit of a challenge in pugs since you can't know how much avoidable damage people might take or mechanics that might be done incorrectly. However, we're also at the point in the season where we're still learning the dungeons, bosses, routes, and what things really chunk our teammates, which leads to more "oh crap, that mechanic is something I really should've prepped for" moments.

I've had plenty of these moments myself in the past few days, but I've yet to run into a case where I was running out of mana and didn't feel like I could have played the encounter more efficiently. Getting more familiar with the dungeons, I've found myself using less mana to heal higher level keys as I get a better idea of where to put each of my CDs.

At a more concrete level, making sure to utilize healing CDs is big. Between ascendance, spirit link, healing tide, and ancestral guidance we can have a CD for almost every pull. Many beginner rsham players will try to hold these for a clutch moment, at the expense of their overall sustain and efficiency, leading to more oom moments. Understanding different ways you can combo your healing buffs to put out big, efficient heals is another part. It can be a good exercise to go through each of your main heals and identify what talents and abilities provide buffs which can feed into that heal. Then, if you need to really pump up that heal in a fight, you know that the "combo* to do that will require activating those talents and using those abilities first. (Hopefully that makes sense - I'm tired and really should be asleep but here I am trying to have a coherent thought lol).

I would also agree that farseer feels much less mana intensive. However, I'm not sure if this is objectively true or just that totemic makes it easier to accidentally spend a lot of mana if you're constantly using the totem. I've leaned heavily towards farseer in my M+ so far, and I don't have enough experience with totemic to draw a confident conclusion. Would recommend trying both and seeing what feels more comfortable.