UID: 11903619 welcomes you again owo
I'll keep it short this time, promise :3
Palatinus has decent coverage in both competitive game modes with flexible supports. She can cover a couple weathers that would normally require multiple-well invested Valkyries as well as covering weathers tailored for IMAGINARY Valkyries.
Let's take a look at her equipment options first!

Equipment
Weapon
Signature Weapon
Midnight Ataegina

Active skill
Point Quasar
SP Cost: 0 CD: 25
Thrust forward to deal 50% ATK of physical damage to a single enemy. If they are not invincible or have the iron body status, the Valkyrie will pick them up and throw them, dealing 90%+1400% ATK of physical damage.
While an enemy is performing certain moves, (i.e a Jonin attempts to block an attempt or a chariot leaping towards the Valkyrie) a counter-attack can be unleashed regardless of the skill’s cool-down. Additionally, the enemy will be interrupted while receiving 20%+800% ATK of physical damage.
Palatinus Equinix bonus
In Knight form (mounted), the active skill is a throw
Guardian - Knight

Under guardian form (unmounted), it becomes a shotgun attack where 3 shots can be unloaded consecutively.

Each of these shots deals 300% ATK of physical damage.
Tapping the active afterwards unleashes a joint blast, dealing 400% ATK of physical damage.
Shield ram blast: 400% ATK of physical damage
Equinox severance joint blast: 3*400% ATK of physical damage.
Passive 1 - Karma Cycle
The user will gain a 15% unconditional crit rate.
Weapon active skill deals a bonus of 30% total damage and 15% physical damage.
Passive 2 - Daybreak Equinox
Gain 20% total damage.
Activating an evasion skill reduces damage from the rear by 35% for 12 seconds. Reactivations will refresh the duration

Alternatives
Abyss flower

Second best option, although as a non BKE user, PE does not get any special effects from it.
Endothermic Lance VF

Early game option.

Stigmata
Signature Set

Top
Gain 30% Physical damage
Upon landing 10 charged attacks, the user will gain 45% crit damage for 15 seconds.
This effect can be refreshed by fulfilling the same condition.
Middle
Increases the user’s total damage by 20%
Evasion skills and retaliations will boost the user’s total damage by 20% for 15 seconds.
As per the top piece, reactivating this effect will refresh its duration.
Bottom
Increases the user's crit rate by 10%.
When any team member triggers a global time fracture, the user will gain 2 SP on a 3-second cooldown.
If the user does this, she will instead boost her own crit rate by 5% for 15 seconds and is refreshable.
2 Set effect
Total damage increases by 30%.
Palatines Equinox bonus: triggering any of the previously mentioned
stigmata effects will grant her the bonuses from every other piece.
Effectively allow her to maintain every effect by only fulfilling one condition!
3 Set effect
Boosts physical damage by 30%
Activating the 2 set effect will boost the physical damage of the user’s next
ultimate attack by 80% and make it restore 200 HP.

Alternatives
Dante Top and Middle + Elysia Bottom

Kafka could also replace Dante in this configuration but the downtime on it doesn’t suit PE’s playstyle.
Elysia Top and Bottom + Marco Polo Middle

Michelangelo Top and Bottom + Marco Polo Middle

About as budget as it can get

Abyss
Main Team Composition

General rotation
1. Herrscher of Sentience Spear combo
2. Carole QTE
3. Charged charged attack + weapon skill (optional)
4. Carole Ultimate
5. HoS Ultimate
6. PE QTE
7. Evade and use Knight Charged Attack + weapon skill (optional)
8. Switch to Guardian Form and perform Charged Attack + weapon skill (optional)
9. Cast Ultimate - This can be cast before or between 7 and 8 when facing imaginary enemies.
10. Rinse and repeat.
Skip HoS and PE's ultimate when both of them are still regaining SP.

Preys
Herrscher of Dominance

Otto Apocolypse

Jizo Mitama

Mobs

Physical Asaaka


Predators
Couatl

Tonatiuh

Bright Knight Excelsis

Both Andrius

Ranged MHT-3B Nirvana

Ranged Asaaka

Both Husk Nihilus


Team Composition
Memorial

Replace Carole with Lightning Empress and have her lead the team for SS bosses.
General rotation
1. HoS chain and spear combo
2. Evade and casting ultimate when there's sufficient SP
3. Cast LE's weapon skill
4. PE evade and charged attack
5. Ultimate if the boss is low, if not perform guardian charged beforehand,

Preys
Herrscher of Dominance

Otto Apocolypse

Jizo Mitama

Kallen Kaslana


Predators
Tonatiuh

Couatl

Benares

Overall, she has very good coverage while taking care of bosses that cater to her kit. It would be worthwhile to build her if IMAGINARY bosses and/or physical bosses pose an issue for you.
Before we go, here's a small bossing compilation showcasing her potential. Disclaimer that they are by no means the top scores she can attain, rather it paints a picture of how much damage she can deal and how to react in different scenarios :p
https://youtu.be/k6MXQMusm04


