I am not a native speaker, but I have managed (from my point of view) to achieve a pretty decent conclusion.

According to Cambridge Dictionary At, on and in (place) (visited 13th December 2021), "in" is used to talk about locations in a larger area, which is the purpose when you are talking about being physically in a bank, as your position within the bank is not explicitly stated.

However, "at" can be used to talk about locations at companies, workplaces when we see them as a place of activity. From what I have been able to understand, given by the example How many people are working at Microsoft?, the place's name can only be a company's name or a term referring to your workplace.

Using this, we could technically say I am at Bank of America. Supposing the two interlocutors know about which bank they are talking about, you could technically say the equivalent phrase, I am at the bank.

So, regarding to the usage of "at" (as the usage of "in" is valid in all three instances), the first and third would be valid depending on whether the other interlocutors knows about the bank we are talking about. The second one should be invalid, as you want to reveal that you are in a bank, but you don't want to specify which one.

However, if the usage of "at" is valid for any term that refers to a company/workplace when we see them as a place of activity, then all three should be valid.

Can any native speaker or English philologist confirm or deny my claims?

I am not a native speaker, but I have managed (from my point of view) to achieve a pretty decent conclusion.

According to Cambridge Dictionary At, on and in (place) (visited 13th December 2021), "in" is used to talk about locations in a larger area, which is the purpose when you are talking about being physically in a bank, as your position within the bank is not explicitly stated.

However, "at" can be used to talk about locations at companies, workplaces when we see them as a place of activity. From what I have been able to understand, given by the example How many people are working at Microsoft?, the place's name can only be a company's name or a term referring to your workplace.

Using this, we could technically say I am at Bank of America. Supposing the two interlocutors know about which bank they are talking about, you could technically say the equivalent phrase, I am at the bank.

So, regarding to the usage of "at" (as the usage of "in" is valid in all three instances), the first and third would be valid depending on whether the other interlocutors knows about the bank we are talking about. The second one should be invalid, as you want to reveal that you are in a bank, but you don't want to specify which one.

However, if the usage of "at" is valid for any term that refers to a company/workplace when we see them as a place of activity, then all three should be valid.

Can any native speaker or English philologist confirm or deny my claims?

Edit 1

After reading the comments and some answers, I am starting to believe that the second option is the correct answer, i.e., all three of them should be valid, as one can see the bank as a place of (financial) activity.

I am not a native speaker, but I have managed (from my point of view) to achieve a pretty decent conclusion.

According to Cambridge Dictionary At, on and in (place) (visited 13th December 2021), "in" is used to talk about locations in a larger area, which is the purpose when you are talking about being physically in a bank, as your position within the bank is not explicitly stated.

However, "at" can be used to talk about locations at companies, workplaces when we see them as a place of activity. From what I have been able to understand, given by the example How many people are working at Microsoft?, the place's name can only be a company's name or a term referring to your workplace.

Using this, we could technically say I am at Bank of America. Supposing the two interlocutors know about which bank they are talking about, you could technically say the equivalent phrase, I am at the bank.

So, regarding to the usage of "at" (as the usage of "in" is valid in all three instances), all these three sentences would be valid depending on whether the other interlocutors knows about the bank we are talking about.

Can any native speaker or English philologist confirm or deny my claims?

I am not a native speaker, but I have managed (from my point of view) to achieve a pretty decent conclusion.

According to Cambridge Dictionary At, on and in (place) (visited 13th December 2021), "in" is used to talk about locations in a larger area, which is the purpose when you are talking about being physically in a bank, as your position within the bank is not explicitly stated.

However, "at" can be used to talk about locations at companies, workplaces when we see them as a place of activity. From what I have been able to understand, given by the example How many people are working at Microsoft?, the place's name can only be a company's name or a term referring to your workplace.

Using this, we could technically say I am at Bank of America. Supposing the two interlocutors know about which bank they are talking about, you could technically say the equivalent phrase, I am at the bank.

So, regarding to the usage of "at" (as the usage of "in" is valid in all three instances), the first and third would be valid depending on whether the other interlocutors knows about the bank we are talking about. The second one should be invalid, as you want to reveal that you are in a bank, but you don't want to specify which one.

However, if the usage of "at" is valid for any term that refers to a company/workplace when we see them as a place of activity, then all three should be valid.

Can any native speaker or English philologist confirm or deny my claims?

I am not a native speaker, but I have managed (from my point of view) to achieve a pretty decent conclusion.

According to Cambridge Dictionary At, on and in (place) (visited 13th December 2021), "in" is used to talk about locations in a larger area, which is the purpose when you are talking about being physically in a bank, as your position within the bank is not explicitly stated.

However, "at" can be used to talk about locations at companies, workplaces when we see them as a place of activity. From what I have been able to understand, given by the example How many people are working at Microsoft?, the place's name can only be a company's name or a term referring to your workplace.

Using this, we could technically say I am at Bank of America. Supposing the two interlocutors know about which bank they are talking about, you could technically say the equivalent phrase, I am at the bank.

So, regarding to the usage of "at" (as the usage of "in" is valid in all three instances), the first sentence should be valid, as you are going there to do an activity (a transaction or something similar).

The second should also be valid, as it can be considered your workplace, a place of activity.

I cannot reach any strong conclusions to the third one.

Can any native speaker or English philologist confirm or deny my claims?

I am not a native speaker, but I have managed (from my point of view) to achieve a pretty decent conclusion.

According to Cambridge Dictionary At, on and in (place) (visited 13th December 2021), "in" is used to talk about locations in a larger area, which is the purpose when you are talking about being physically in a bank, as your position within the bank is not explicitly stated.

However, "at" can be used to talk about locations at companies, workplaces when we see them as a place of activity. From what I have been able to understand, given by the example How many people are working at Microsoft?, the place's name can only be a company's name or a term referring to your workplace.

Using this, we could technically say I am at Bank of America. Supposing the two interlocutors know about which bank they are talking about, you could technically say the equivalent phrase, I am at the bank.

So, regarding to the usage of "at" (as the usage of "in" is valid in all three instances), all these three sentences would be valid depending on whether the other interlocutors knows about the bank we are talking about.

Can any native speaker or English philologist confirm or deny my claims?