TL;DR

• Straightforward Blaze Artillery spam playstyle; can spam your Grenade Fans too or instead if you prefer.
• If you have Arcane Steadfast, feel free to replace Energize with it - it's better for the spammy playstyle this build is intended for and also cheaper to get.
• [Archon Vitality] is nice to have because it significantly boosts [Blaze] Artillery's output, but don't worry too much if you don't have it, especially if you're more focused on something like Grenade Fan anyway.
• No survivability because this is a mostly shieldgate build, greatly aided by her Grenade Fan in its shield satellite form.

Notes

NOTE: [Archon Stretch] is only relevant if you go with Coil Horizon for your subsume! Big part of why I picked this subsume in particular over other grouping options. If you run something else, you can drop Archon Stretch and save a forma!

NOTE 2: I finally have added in rank 0 Archon Vitality as of 12/19/2023 - it's a massive boost for [Protea]'s turrets, giving you EVEN MORE (double!) damage per hit. If you don't have it, you can substitute in Augur Message at rank 4/5 for the exact same amount of mod drain, leaving you with enough energy at mission start to put down your Dispensary.

NOTE 3: Why Steel Charge? It's honestly a crappy aura choice. I picked this solely because I wanted to do something on a 0-forma budget and this aura gives me enough extra mod space to fit on everything I want without formaing (if one skips [Archon Stretch] and uses regular [Stretch] instead). However, if you care about [Protea], I recommend you forma some of your mods and give her a more useful aura, like [Corrosive Projection] or what have you.

NOTE 4: Beware that using Augur mods overrides [Protea]'s extra shield gate duration from her shield satellites. I use Augur mods anyway because I like the extra range and strength more than I mind losing the extra gate duration, but keep this in mind and be aware of it for your own playstyle - if you need to, you can drop the two Augur mods for something like utility (e.g., [Rolling Guard]) or alternate sources of these stats (e.g., [Power Drift]).

Strategy

[Augur Message] is intentionally left unmaxed to ensure you have just enough energy at the start of ANY mission besides one with an energy drain modifier (but including those with energy reduction modifiers!) to drop Dispensary down, if you're allergic to energy pads like I am. Totally fine to max out and pop an Energy Restore (yum, pizza) or Zenurik's Wellspring at the start of a mission instead, though.

Begin by dropping Dispensary anywhere. Arcane Energize makes sure your energy's always full when combined with this ability; since [Protea]'s playstyle is pretty spammy, Arcane Steadfast is a nice sidegrade to it. If you can't or don't want to use this arcane, one or a combination of Emergence Dissipate (equipped on your Drifterator), amber shards, and [Equilibrium] (probably best slotted over [Constitution]) will help instead.

I recommend inverting controls for [Protea] so you can tap 1 anytime for her shield grenades, giving you constant overshields (which is your survivability in this build).

The rest of the strategy is just to spam [Blaze] Artillery (and slash grenades, if you so choose) and clear rooms on pretty much any mission difficulty, from Sorties to Steel Path. [Double Tap] your subsumed Coil Horizon whenever you want to drag in more enemies (double tapping helps you control where it lands, but feel free to tap later or let it auto-finish if you're comfortable with the bounce!). Use either Blaze Artillery or Dispensary anytime your passive is at the 100% strength bonus. Blaze Artillery has built-in CC via constant heat procs, which is nice. Together with that, Coil Horizon adds a second proc type for your Condition/Gundition Overload needs, if you go with that for your subsume.

The first Arcane can be replaced by Arcane Steadfast these days, and in fact it's the better option - I just haven't gotten around to playing with it much personally.

The second Arcane is a flex slot; Molt Augmented is a nice option for longer runs, for example. I used to run [Fury] because I enjoy melees, even though this build doesn't need melee play at all. Molt Efficiency works nicely on her because more duration is welcome on almost the entirety of her kit here.

I used to have Roar, then Pillage, infused on her 4th ability slot. Currently, I have Coil Horizon instead - grouping is great with [Protea] thanks to the way it boosts her [Blaze] Artillery damage multiplier, which increases per hit dealt. I chose Coil Horizon for the flavor, [Archon Stretch] synergy, and extra status proccing; you may prefer other grouping abilities, so experiment and see what you like!

If you don't want to or can't infuse a different ability onto her 4, that's fine. I personally find her default 4 to be jank as a nuke, utility, or survival tool, though it's worth noting that its augment - Temporal Anchor - provides nice armor strip synergy with Blaze Artillery. If you can fit it on the build, go for it!

I pair with Vazarin for a free oh-shit immortality button in case shield grenades ever go down. Feel free to use Madurai for Madurai things, Unairu for Caustic Strike's armor strip, or Zenurik for an excess of energy via Wellspring.

Stats breakdown

200% duration gives 6 seconds per Blaze Artillery, which I find to be convenient for re-positioning guns if needed, as well as for letting them build up decently in damage scaling ([Blaze] Artillery gets a damage multiplier that increases with every enemy hit by [Blaze] Artillery).

Somewhat high power strength (168% in this case, but feel free to experiment) because I find it strikes a nice sweet spot between the guns' base damage on cast and their per-hit scaling potential, especially when combined with [Protea]'s passive strength boost. High range to let the guns cover even big rooms (or expanses like those in open worlds; have done many a Deimos Steel Path bounty with these bad boys).

130% efficiency is a nice QoL as well, permitting me to pop Dispensary at the beginning of any mission. I didn't use (Primed) [Flow] because Dispensary and Energize already keep [Protea]'s bar filled for all the ability spam she might want to do with this build.

No survivability mods other than [Handspring] (for the stray knockdown in higher levels) because between the innate CC her [Blaze] Artillery gives and shield gating, her shield grenades handily take care of surviving.

Where can (or should) I use this build?

Anywhere really. I've used this in solo play (and squad play, too) on Steel Path missions from survival to mobile defense to defense and more. I use it whenever I don't know or care what to bring. It's a very Swiss Army knife build, offering CC, DPS, survivability, self and squad healing, self and squad shielding, self and squad energy restore, AND self and squad universal ammo restore. The only things she can't do are go incredibly fast or turn invisible, basically.