"Merci" meaning "please" or "veuillez"

Merci de expresses a recommendation [c.f. A.2.a)] whereas veuillez implies an injunction.

Both sentences formulate a request: recommendation/injunction.

Using this would be polite formula is not recommended in the context you present; it is barely acceptable as an introduction of routine requests in application forms and the like. It is otherwise considered as manipulative and inelegant, not polite: you extend thanks to someone before you've even had a reaction to what you just asked (non au merci de…).

Here are more recommendations not to use this formula.

https://www.helloworkplace.fr/merci-de-ne-plus-ecrire-merci-de-dans-vos-mails-et-autres-impolitesses-au-bureau/

https://optimiz.me/2-formues-de-politesses-a-proscrire-de-vos-e-mails/

The word please can be written in more than one way in French, which all have small differences in meaning. It's why you see the word « Merci » used that way.

All the forms in the sentence example you gave:

• Merci de...
• Prière de...
• Je vous prie de...
• Veuillez...

The vouvoiement makes the sentence that way, it's extra-polite. It's a concept that doesn't exist in English I think.

So as I said, in the sentence you could swap the word « Merci » with « Prière ».

Example:

Prière de vous enregistrer au moins une heure avant de partir.

The sentence means the same thing, but the word « Merci » is softer in tone, where in the example I gave it's a more direct way to say it.