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You learn its properties

The vessel is a "magical vessel" and a "tiny object", so it qualifies as a "magic-imbued object" for Identify. Thus the caster learns its properties: basically all of the text describing it on the page.

As a DM, I'd rule that which warlock it belongs to and which genie provided it falls under its properties, as well as whether the warlock is currently residing in it and whether it has any objects stored in it.

However, none of this information might be available if the vessel is under an illusion such as Arcanist's Magic Aura, which a clever DM or Warlock might use for story reasons.

You learn its properties

RAW

The vessel is a "magical vessel" and a "tiny object", so it qualifies as a "magic-imbued object" for Identify. Thus the caster learns its properties: basically all of the text describing it on the page.

Up to interpretation

As a DM, I'd rule that which warlock it belongs to and which genie provided it falls under its properties, as well as whether the warlock is currently residing in it and whether it has any objects stored in it.

Warlock it belongs to may also fall under "how to use it" because to use it you must be that warlock. Learning the number of charges implies you learn about its magical state, so I think learning the Genie who owns it and if the warlock is inside seems reasonable.

A DM would be well within reason to not reveal this information. If your worried about a player casting this on your lamp, talk to your DM

Other magic may intervene

However, none of this information might be available if the vessel is under a spell like Nondetect or, depending on interpretation, Arcanist's Magic Aura, which a clever DM or Warlock might use for story reasons.

You learn its properties

The vessel is a "magical vessel" and a "tiny object", so it qualifies as a "magic-imbued object" for Identify, so the caster learn its properties: basically all of the text describing it on the page.

I'd rule as a DM that which warlock it belongs too and which genie who provided it falls under its properties, as well as whether the warlock is currently residing in it and any objects stored in it.

Unless the vessel is under an illusion such as Arcanist's Magic Aura which a clever DM or Warlock might use for story reasons.

You learn its properties

The vessel is a "magical vessel" and a "tiny object", so it qualifies as a "magic-imbued object" for Identify. Thus the caster learns its properties: basically all of the text describing it on the page.

As a DM, I'd rule that which warlock it belongs to and which genie provided it falls under its properties, as well as whether the warlock is currently residing in it and whether it has any objects stored in it.

However, none of this information might be available if the vessel is under an illusion such as Arcanist's Magic Aura, which a clever DM or Warlock might use for story reasons.

You learn its properties

The vessel is a "magical vessel" and a "tiny object", so it qualifies as a "magic-imbued object" for Identify, so the caster learn its properties: basically all of the text describing it on the page.

I'd rule as a DM that which Genie and Warlock it belongs to falls under its properties, as well as whether the Warlock is currently residing in it.

Unless the vessel is under an illusion such as Arcanist's Magic Aura which a clever DM or Warlock might use for story reasons.

You learn its properties

The vessel is a "magical vessel" and a "tiny object", so it qualifies as a "magic-imbued object" for Identify, so the caster learn its properties: basically all of the text describing it on the page.

I'd rule as a DM that which warlock it belongs too and which genie who provided it falls under its properties, as well as whether the warlock is currently residing in it and any objects stored in it.

Unless the vessel is under an illusion such as Arcanist's Magic Aura which a clever DM or Warlock might use for story reasons.