Protea is a very versatile frame that can be modded for different scenarios. This is my preferred non-temporal anchor Protea build that doesn’t require specific weapons/companions to excel at. More duration focused to make the most out of all of her abilities as well as keeping positive strength and duration.

Check out an this build for my preferred temporal artillery play style: https://overframe.gg/build/739585/protea-prime/sticky-turret-cheese-build/

You can use grenade fan for minor CC but mainly as shield [Regen] and general survivability. Turrets for damage and clearing enemies, dispensary for energy and ammo. Utilise her passive to get the most out of dispensary and subsumed abilities. (Or temporal anchor)

Since this is a non [Temporal Artillery] build, I have elected to subsume over her 4th in favour of abilities that can buff her turrets(her main source of damage and kills).
Generally, roar is probably the best ability to replace her 4th with since it is a faction dmg buff for both weapons and abilities and can also buff allies. However, there are other options for subsumes if you prefer:

• Roar (faction dmg buff for both weapons and abilities, can buff allies, probably the best out of these options)
• Pillage (good armour strip when paired together with her passive, more active play style, need Corrosive Projection for aura)
• Coil Horizon (easy and better grouping than Larva or Ensnare in my opinion) or other grouping abilities
• Nourish (free viral for weapons and energy, can replace equilibrium for something as well, but won’t buff turrets)
• Gloom (Gloom)
• Tempest Barrage (paired with Viral tempest and/or emerald shards to make viral CC armour strip zones)

[Precision Intensify] is a flexible slot. Replace it depending with whatever stat that you want or need(range, duration, etc)

If you want to use temporal anchor with its augment, replace precision intensify with Temporal Erosion/[Temporal Artillery].

Arcanes are flexible, but there aren’t many options that can help [Protea]. I recommend Molt Augmented and Efficiency.

Archon shards are highly recommended. I prefer to slot:

3x Amber (really important IMO)
2 for casting speed, 1 for energy on spawn

2x Crimson (not needed but helps)
can be either duration or strength or even both

There are alternate ways to get the extra buffs from shards from other sources such as focus schools and Tome mods, but I prefer not requiring an external source to get them. Nonetheless, fine tune your build and setup to your preference.

Notes:
I see many people make the same mistake when building [Protea] and it really has to be said. DO NOT PUT AUGUR MODS OR [Brief Respite] ON [Protea], unless you dont really care or are going to subsume her 1st ability(why would you do this?) This is because when a shield satellite that is connected to your warframe and a shield gate(a brief invulnerability period when your shields are depleted)triggers, its duration is supposed to be doubled(around 3-5 seconds of pure invulnerability), instantly destroying the connected satellite. However, because of how augur mods and [Brief Respite] function, the doubled invulnerability duration will be overridden with the normal duration. Since [Protea]'s main survivability is through shield tanking and gating, the extra duration is extremely helpful for her survivability, especially in higher level missions.