Hey there.
Shamans are very reactive healers, so you’re on the right track. I’ve played mine for 10+ years, not out of enjoyment, but out of dedication and loyalty.
Long story short: You’re going to excel in stacked group healing, but you’re going to have to struggle more than others in Mythic+ just like in BfA. Why is that? Lack of damage reduction cooldowns for your tank and inconsistent single-target healing. Earth Shield being baseline has helped a bit on that front, boosting all healing done to Earth Shielded targets. Your main strength is your utility, which means your Earth Element, your Capacitator Totem, Tremor Totem, your Wind Shear, Heroism/Bloodlust and your high DPS potential with Flame Shock and Lava Burst.
Once you’ve played through a few dungeons, you’ll begin to notice the shortcomings of the spec, such as dealing with spread out group healing when people aren’t stacked and keeping the tank alive while you’re dealing with group-wide damage. From my first impression, having done my 8 Mythics in Shadowlands, I would say that Restoration is stronger in SL than it was in BfA. It is definitely going to be viable in higher mythic keys, but it’s not going to be a prioritized pick for the end-game, or in any Mythic+ competitions.
You’re still going to be topping the meters in raids, and you’ll do just fine on non-stacked fights with a lot of movement. Something like your Spirit Link Totem is going to be crucial in raids as well, especially for progression, along with Wind Rush Totem, so you’ll feel very useful.
In terms of playstyle, I’m not really sure how to describe it. It’s personal preference, after all. You’ll be standing still a lot to cast, as your heals have quite long cast times. This can be helped by higher levels of haste, but haste is not something you’re going to prioritize. You’ll be going for crit for the mana regen and throughput, and versatility for the flat throughput and damage reduction (especially in dungeons). For raids, you can prioritize haste/mastery instead of versatility.
As for PvP, I haven’t done much of it since Cataclysm, so I can’t speak on that, but from what I’ve seen it’s very viable. I watch Cdew’s stream a lot, and he does very well on Resto Shaman. Not so much in battlegrounds, it’s definitely an arena spec. All you have in terms of damage reduction is your Astral Shift, so they’re definitely one of the squishier healers in arena, so just make sure you play with classes who can peel for you and support you, so you don’t get trained, which has been a big problem for Shamans in arena for the last 8 years.
I think that about covers it. Let me know if you have any questions.