[RPG] Can non-concentration spells with a duration be cast multiple times from one Spellwrought Tattoo

The errata for the PHB answers this question definitively:

If a Wild Magic effect is a spell, it’s too wild to be affected by Metamagic. If it normally requires concentration, it doesn’t require concentration in this case; the spell lasts for its full duration.

So no concentration is required, and the spell will last for its full duration.

Only select feats associate their spells with a class

Let's look at the Sorcerer's Spellcasting feature:

[...] The Sorcerer table shows how many spell slots you have to cast your sorcerer spells of 1st level and higher. [...]

From this we can conclude that the spell slots from the Sorcerer class can be used to cast a spell only if that spell is a Sorcerer spell (whatever that means).

The Sage Advice Compendium (pdf link) states the following about the Magic Initiate feat (emphasis mine):

Q. If you have spell slots, can you use them to cast the 1st level spell you learn with the Magic Initiate feat?

A. Yes, but only if the class you pick for the feat is one of your classes. For example, if you pick sorcerer and you are a sorcerer, the Spellcasting feature for that class tells you that you can use your spell slots to cast the sorcerer spells you know, so you can use your spell slots to cast the 1st-level sorcerer spell you learn from Magic Initiate. [...]

In short, you must follow your character’s normal spellcasting rules, which determine whether you can expend spell slots on the 1st-level spell you learn from Magic Initiate.

From this we can conclude two things:

1. A spell granted by a feat that explicitly links the spell to a given class is associated with that class (a Sorcerer taking Magic Initiate under Sorcerer and choosing to learn magic missile can use their spell slots to cast magic missile; therefore, magic missile must be considered a Sorcerer spell).

2. A spell that is granted by a feat and appears on our class spell list is not necessarily associated with our class (a Sorcerer taking Magic Initiate under Wizard and choosing to learn magic missile cannot use their spell slots to cast the spell; therefore, magic missile must not be considered a Sorcerer spell).

Thus, most spells gained from feats are not associated with any class whatsoever. The most notable exception is Magic Initiate, which associates the spell with whichever class you pick. Other examples would be Ritual Caster and Spell Sniper as well as the Wood Elf Magic feat's cantrip in particular which is required to be a Druid cantrip.

The feat in question does not associate the spells learned from it with a particular class; thus they do not count as class spells for whoever is casting them and they are not subject to various requirements or usable with various abilities that say "When you cast a {class} spell..."

Instead, what this feat says is:

[...] You can also cast these spells using spell slots you have of the appropriate level. The spells' spellcasting ability is the ability increased by this feat.

This means that you are explicitly able to use your spell slots on these spells (a rather rare thing), however they are not associated with your class. This is especially clear given that their spellcasting ability need not be the same as the one your class actually uses, though even if they were the same, this would still be the case.

A big list of related questions

That all said, ultimately, whether a given spell is associated with your class and considered a class spell is up to the GM. We have several questions on this (and related topics) with numerous differing answers:

• What makes a spell being cast considered to be a {class} spell?
• Are spells learned from feats considered to be associated with your class?
• What is an "artificer spell" for Infuse Magic?
• Does Confusion cast via the Dreadful Word invocation count as a warlock spell?
• Can the artificer's spell-storing item store their specialist spells?
• Can I use my best spellcasting ability for Eldritch Adept?
• If I am a Celestial Warlock and I take the Magic Initiate - Cleric (Cure Wounds), does that now count as a Warlock spell for me? [duplicate]
• What counts as a sorcerer spell for the purposes of the Wild Magic sorcerer's Wild Magic Surge feature? [duplicate]

• Can a sorcerer spell cast from a magic item trigger a Wild Magic Surge?
• Could a Wild Magic Surge be triggered by a Wild Magic Sorcerer using a Magic Initiate spell?
• Wild Magic Surge activation without using spell slots
• For Ring of Spell Storing, when does Wild Magic Surge trigger?
• Can the 1st-level spell learned through the Aberrant Dragonmark feat trigger a Wild Magic Surge?
• Does Wild Magic Surge trigger off of spells on the Sorcerer spell list, if I learned them from another class?
• Can you cast a spell learned from the Magic Initiate feat using spell slots?
• Can you trigger Wild Magic Surges with rituals?

• If you have the ability to cast a spell without a spell slot, can you cast that spell using a spell slot?
• Can I use spell slots to cast the spell granted from the Fey Teleportation feat additional times?
• Does Magic Initiate allow the chosen spell to effectively be "always prepared" if the spell is on their spell list?
• If I take the Magic Initiate feat and choose a different class, but pick a spell that's also on my class's list, can I cast it using spell slots?
• Can an Arcane Trickster or Eldritch Knight with the Magic Initiate feat (picking the wizard list) use spell slots to cast the chosen 1st-level spell?

• Does casting a spell from an item allow you to apply class abilities that are used when casting a spell?
• Can a spell being cast via a magic item be considered to be more than one class' spell at the same time?
• Can you retrain the Magic Initiate spell using the Spellcasting feature?
• Can spells from the Magic Initiate feat be swapped out for different ones?
• As a Sorcerer, can you trade out the spells granted by the Drow High Magic feat?
• Does the "Cantrip Formulas" optional Wizard feature allow a racial cantrip to be swapped for another?