How do Eberron dragonmarks' Spells of the Mark interact with the Pact of the Tome warlock's Book of Ancient Secrets invocation?

Question

I might be over-analyzing and confusing myself, but I'm not certain regarding the interaction between dragonmark-learned Ritual spells and the Book of Ancient Secrets warlock invocation.

Let's take as an example the Mark of Hospitality subrace's trait:

Spells of the Mark. If you have the Spellcasting or the Pact Magic class feature, the spells on the Mark of Hospitality Spells table are added to the spell list of your spellcasting class.

This list includes ritual spells like, Leomund's tiny hut, Mordenkainen's private sactum and hallow.

Now let's take the Book of Ancient Secrets eldritch invocation:

You can now inscribe magical rituals in your Book of Shadows. [...] You can also cast a warlock spell you know as a ritual if it has the ritual tag.

On your adventures, you can add other ritual spells to your Book of Shadows. When you find such a spell, you can add it to the book if the spell’s level is equal to or less than half your warlock level (rounded up) and if you can spare the time to transcribe the spell. For each level of the spell, the transcription process takes 2 hours and costs 50 gp for the inks needed to inscribe it.

In order to ritual-cast these spells (added to my spell list by the dragonmark) as non-prepared spells, but rather as ritual spells from my Book of Shadows, which of the following mechanism is appropriate, per RAW (and/or RAI):

1. They count as warlock spells (by being added to my spell list as per the spells of the mark trait), and thus I can cast them without preparation since they have the ritual tag (as per the Book of Ancient Secrets invocation).
2. I magically learn them (as per the Spells of the Mark trait) but I have to spent time to transcribe the spell in the Book of Shadows, although I don't have a physical written form of the spell.
3. It does not satisfy either mechanism, and the only way to cast these spells is to prepare them as warlock spells, until I find them in written form and can transcribe them in the Book of Ancient Secrets.

Which of the above interpretations is correct, if any?

Answer 1

1) Yes, these spells count as warlock spells for you

As the Mark feature states:

Spells of the Mark. If you have the Spellcasting or the Pact Magic class feature, the spells on the Mark of Hospitality Spells table are added to the spell list of your spellcasting class.

2) You do not automatically learn these spells, the feature does not say so

Nothing says that you learn these spells automatically. You can either learn them as warlock spells when you level up, the same way you would learn any other spell or if they are ritual spells and fulfill the level requirement, you can transcribe to your book the same way you would any other ritual if you have a written copy of the spell.

Regardless of the way you choose you can cast them as a ritual, but casting them not as a ritual requires you to learn them on level up as a warlock spell.

3) Warlocks spells you know are automatically prepared. To learn them, you pick them on level up. In addition, you can transcribe rituals to your book if you have a copy of them and then cast them ritually.

Answer 2

They work the same way as Patron spells

Mark spells use the same mechanism as the Patron spell lists, meaning the spells are added to your class list and are warlock spells for you.

• This does not make them automatically prepared or castable. If the feature did that, it would say so. You can (and have to) learn them as you learn any other warlock spell.

• To add them to your book you would need to find a written copy of them.