Okay, I had a look over the class and my initial reaction is "best of both worlds" syndrome.
When creating a "hybrid" it's too easy to want to take all the best pieces from a class, and grant it to the new hybrid because you feel if each class can have the abilities it wont be overpowered. Unfortunately this leads to power creep (weak powers are essentially disadvantages in the grand scheme of things, even if they grant a benefit).
On a point by point basis I would consider revising the following:
1. I would consider removing the armour benefit from this class. A Messiah needs self-belief that his Deity will shield him from blows. Instead, grant him the following ability:
"Faithful Aura. While wearing no armour and using a shield, your armour class is equal to your 10 + your dexterity modifier + your charisma modifier." Now, I understand this might lead to a higher AC at low level (allowing for a 16, versus a 15 with light armour) but it prevents shield usage, and requires Charisma/Dex to progress in terms of armour class.
2. I would remove the musical instruments from the class, I don't believe someone focusing on a career as an Orator would require instruments.
3. I would suggest Wisdom and Charisma, similar to a Cleric (because it's a faith-based class and you require mental resilience. I agree an argument for Constitution could be made as well).
4. Weapons I would limit to Simple weapons only. I don't believe they would consider learning how to wield a longsword as part of their devotion.
5. Don't force skills on people. Religion is about past knowledge, not the future. Studying your deity isn't really mandatory, and I also don't think the class can be justified having access to 3 skills. (3 skills is usually reserved for stealth characters).
Moving on to the class abilities:
1. rename Blessing to Pious Inspiration. The Inspiration label will let people know "it's Bardic Inspiration by another name." Font of Inspiration would remain at 5th.
2. I would consider leaving off Channel Divinity, and simply creating a new ability instead. So far only characters who can turn Undead can Channel Divinity. I would consider a similar power but just reflavour it, for example: Purge the Heresy. Every hostile creature within 60' must make a Wisdom saving throw or suffer from the weight of their sins. Any creature who fails their saving throw suffers 3d6 Psychic damage and is Frightened for 1 minute. At the end of each round they may make a new saving throw to shrug off the Frightened effect.) You can consider increasing the damage somehow, possibly 1d6 every 4 levels, because the frightened always remains strong.
3. Divine Patronage is just too powerful. I am not sure when it is gained, but it's basically IDDT IDKFA cheat codes. I would revise this entirely.
When it comes to the Archetypes, I would consider slimming it down to 2 only, unless you want multiple with similar principles. Most classes with more than 2 Archetypes have them using the same mechanics, simply different spell choices (Fighter's Champion really doesn't count as a full archetype!)
I would recommend merging Saint and Prophet into a single Archetype, because, again, too many abilities are being lifted from elsewhere simply because they're awesome (even if they may fit).
So if you merge them into 2 I would recommend going with Flagellant and Martyr (Martyr is a good fit for the caster-focused one as both would signal they are prepared to die for their cause!)
The Flagellant
Since I recommend removing Channel Divinity, you can change Righteous Wrath into a reactionary ability:
Eye for an Eye: At 3rd level, when you suffer damage from a creature within 30', you may use your reaction to deal profane damage equal to the damage dealt. (renaming of Righteous Wrath)
You gain proficiency in Martial Weapons.
Zealotry: Your attacks deal an additional damage dice of the same type. At 14th level this increases to 2 dice.
Bloodied Warrior: At 10th level you are capable of surviving the harshest wounds from your years of self mutilation. While you are under 50% health you have resistance to all damage from weapon attacks.
Righteous Fervour: At 14th level the devotion to your deity drives those around you to fight long after they should be capable of. When a creature within 60' is reduced to 0hp, you may expend a use of Pious Inspiration to reduce them to 1hp instead. Once you use this ability you require a long rest to use it again.
Martyr:
Sermon. At 3rd level your messages inspire those around you. When you grant another creature Pious Inspiration their next successful attack before your next turn deals additional damage equal to your charisma modifier.
Benevolent Gift. You gain access to 1 cantrip from any spell list which requires an attack roll.
Forceful Personality. At 6th level, you may add your charisma modifier to any cantrip damage.
Convert the Masses. At 10th level you may expend a use of Pious Inspiration to attempt to charm all creatures within 60'. While charmed, their speed is reduced to 0 and they are treated as prone, while they drop to their knees to worship the new deity. At the end of each round they may make a new saving throw against this effect. The effect is automatically broken if they suffer any damage from you or your allies.
Strengthen the Believers. At 14th level you reinforce the mental resolve of those around you. When you use Pious Inspiration on a creature, it may immediately make an intelligence, wisdom or charisma saving throw against any 1 spell currently affecting it. If no such spell is active, the creature gains advantage on it's next one within 10 minutes.
The reason I changed it to 3/6/10/14 is so they don't receive quite so many abilities, causing you to struggle what to give them. I also removed extra attack because you would then be allowed both 2 attacks AND a bonus action to use spiritual weapon, which is why Clerics do not receive it.
As for the spell list, I think if you choose to cherry pick cleric/bard spells it is important to focus on what you don't get. For example, I agree Spiritual Weapon is a good idea (which is the main reason you should not give this class Extra Attack, as your Bonus Action is free to deal damage on top of a couple of hefty blows).
Cantrips:
Blade Ward, Light, Message, Guidance, Mending, Resistance, Spare the Dying, Thaumaturgy.
1st Level:
Bane, Bless, Charm Person, Command, Create of Destroy Water, Cure Wounds, Detect Evil or Good, Detect Magic, Detect Poison or Disease, Dissonant Whispers, Feather Fall, Guiding Bolt, Healing Word, Hellish Rebuke, Heroism, Inflict Wounds, Purify Food and Drink.
2nd Level:
Aid, Augury, Calm Emotions, Detect Thoughts, Enhance Ability, Enthrall, Hold Person, Lesser Restoration, See Invisibility, Silence, Spiritual Weapon, Suggestion, Zone of Truth.
3rd Level:
Beacon of Hope, Clairvoyance, Counterspell, Create Food and Water, Dispel Magic, Fear, Fly, Mass Healing Word, Remove Curse, Sending, Spirit Guardians, Tongues, Water Walk
4th Level:
Banishment, Compulsion, Confusion, Control Water, Divination, Freedom of Movement, Guardian of Faith, Locate Creature.
5th Level:
Commune, Contagion, Dispel Evil and Good, Dominate Person, Dream, Flame Strike, Geas, Greater Restoration, Hallow, Hold Monster, Mass Cure Wounds, Scrying, Teleportation Circle.
6th Level:
Find the Path, Forbiddance, Heal, Harm, Heroes' Feast, Mass Suggestion, True Seeing.
7th Level:
Divine Word, Etherealness, Fire Storm, Forcecage, Regenerate, Teleport.
8th Level:
Dominate Monster, Earthquake, Holy Aura, Mind Blank, Power Word Stun.
9th Level:
Foresight, Power Word Heal, Time Stop, Wish.
The spell list focuses on Retributive magic (which is why hellish rebuke is there) curative magic, anything which controls another creature (non-damage) as well as a few "furious" spells from the cleric list, such as flame strike. The key omissions are anything which focused on the dead, because a Messiah only cares about current followers - if they die, they're of no use!
Anyway this is just my suggestion to help improve the class in terms of both balance, and a more general focus.
. This class also completely replaces clerics in my world (since the gods have been forgotten for eons and no one believes in them anymore) and i found it a bit lazy to just refluff the bard.
