Some doubt about the verb "meet"

There are a couple of ways to interpret the form here:

1. Be-perfect - an archaic version of the perfect aspect that uses a form of to be instead of to have.

2. Stative verb and participle - basically, interpreting meet as a past participle describing the state of the participants.

Be-Perfect

English today forms the perfect aspect with the auxiliary verb to have and a past participle. Often, actions put in present perfect have continued to happen through the present moment:

I have joined you for some tea. (present perfect; for more information, see Wikipedia)

However, in some older texts and higher registers in English, the perfect aspect is formed using the verb to be with a past participle:

He is risen. (This is from the Paschal Greeting; more information in "Is 'He is risen' correct?").

Applying the same thinking, you could read this as a use of perfect aspect that adopts a more austere register, appropriate for identifying that they have now met (or are currently meeting) on a battlefield.

Stative verb

Another possibility is to read the verb as a past participle with a stative verb (to be) describing the present situation. To elaborate on this possibility, I will use the extended context of the surrounding sentences in the Gettysburg Address:

Now we are engaged in a great civil war, testing whether that nation, or any nation so conceived and so dedicated, can long endure. We are met on a great battle-field of that war. We have come to dedicate a portion of that field, as a final resting place for those who here gave their lives that that nation might live.

In the first sentence, we are engaged in... could be construed as another be-perfect. However, this is not an archaic usage; engaged as a past participle can also be used to describe a specific state, like a marital engagement ("We're engaged!") or large coordinated efforts ("The US is engaged in a massive effort ..."; "The US is 'engaged in a new era of competition'"; "the front line is the area where each side's forces are engaged in conflict"). So this isn't merely the case of an archaic perfect tense form, but is rather a description of a present state. The Cambridge Dictionary treats this usage of engaged as an adjective, and past participles can function as adjectives in general.

If that is so, then perhaps met can also function as a past participle with a stative verb. Such a usage would be less common, but not unknown (compare well met). Taking the two usages as an example of parallelism, if we are engaged means we are in a state of engagement, then we are met means we are in a state of meeting.

That explanation would also help distinguish why the next sentence is in regular present perfect tense instead of working in parallel with the previous sentence:

We have come [not are come] to dedicate a portion of that field ...

Rather than shifting from one form of present perfect usage to another, this sentence could also draw a contrast from possibly stative uses (the state of the country, the state of those gathered) to an unambiguously active use: we have come. That provides a bridge to the next paragraph and its series of active verbs: "we can not dedicate, we can not consecrate, we can not hallow this ground."

The point

Reading the example as a form of present perfect is the standard reading. That is certainly what this sentence diagrammer suggests, for instance. Yet reading it generically as a stative verb + participle is an understandable reaction, especially within the larger context of the paragraph and following the first sentence. That second interpretation would help explain how the paragraph uncoils from establishing the current situation to state the purpose of the people gathered at Gettysburg.